(Soft music plays)

A title screen over a blue sky reads, Today’s Junior Lesson: Predicting Through Probability.

A female announcer says,

WELCOME TO

TVOKIDS POWER HOUR

OF LEARNING.

A brown haired woman wearing glasses and a leopard print shirt, sits at a table in her home.

A black and white photograph of downtown Toronto hangs on the wall behind her.

The woman says, HELLO, STUDENTS. HOW ARE YOU?

WELCOME TO ANOTHER EPISODE OF

TVOKIDS POWER HOUR OF LEARNING.

A caption appears that reads, Junior 4-6. Teacher Vanessa.

The woman continues, MY NAME IS TEACHER VANESSA,

AND I'M SO EXCITED TO SPEND

THE NEXT 60 MINUTES TOGETHER

LEARNING, HAVING A LOT OF FUN,

AND SHARING A FEW LAUGHS

TOGETHER.

BUT BEFORE WE BEGIN,

I'M HOPING THAT

YOU'VE BEEN PRACTISING

OUR POSITIVE AFFIRMATIONS THAT

WE LEARNED A FEW WEEKS AGO.

THESE ARE POSITIVE STATEMENTS

CALLED MANTRAS,

AND THEY HELP US BUILD

OUR SELF-CONFIDENCE

BY REPEATING THEM

OVER AND OVER EACH DAY.

SO, I'M GOING TO TELL YOU

OUR THREE MANTRAS,

AND I WOULD LOVE FOR YOU

TO REPEAT AFTER ME.

ARE YOU READY?

I AM CAPABLE.

LET ME HEAR YOU.

Vanessa holds her hand to her ear.

I AM A MATH PERSON.

GOOD JOB. AND I CAN DO IT.

AWESOME. I CAN HEAR YOU

ALL THE WAY FROM STONEY CREEK.

SO, TODAY WE'RE GOING TO BE

TALKING ABOUT PROBABILITY.

WHAT ARE THE ODDS

OF SOMETHING HAPPENING?

AND BEFORE WE BEGIN,

I WAS THINKING THAT

I COULD BRING MY SON CHASE OUT

TO PLAY A PROBABILITY GAME

AND GET US WARMED UP

FOR SOME GREAT LEARNING

OVER THE NEXT HOUR.

A young brown-haired boy, Chase, hops behind Vanessa. He wears a black T-shirt

Vanessa says, WELCOME, CHASE.

COME ON IN.

SO, WHAT WE'RE GOING TO

BE DOING--

JUST STAND BESIDE ME,

RIGHT HERE.

RIGHT HERE,

ON THE TABLE.

ARE YOU READY TO PLAY

A MATH GAME?

A caption reads, Junior 4-6. Chase.

Chase says, YEAH!

Vanessa says, OKAY. SO, STAND UP

NICE AND STRAIGHT

SO EVERYBODY

CAN SEE YOU.

OKAY. SO, I AM GOING TO

ROLL A DICE,

AND WHATEVER NUMBER

WE LAND ON,

THAT'S HOW MANY

EXERCISES--

YEAH. ARE YOU READY

TO SHOW THE KIDS

SOME EXERCISES?

SO, BEFORE YOU BEGIN,

MAKE SURE THAT YOU HAVE

A BIG SPACE

TO DO SOME EXERCISES,

JUST LIKE CHASE IS.

MAKE SURE

YOU CAN SPREAD OUT

AND HAVE A LOT

OF ROOM.

SO, WE'RE GOING TO

GET OUR BODIES READY

SO THAT OUR MINDS

WILL BE READY TO LEARN.

I'M GOING TO ROLL

THE FIRST DICE,

AND IT LANDS ON

A FOUR.

Vanessa holds up a large die made of brown cardboard paper.

Vanessa says, SO, CHASE, DO YOU MIND

DOING FOUR JUMPING JACKS?

Chase does jumping jacks and counts, OKAY. ONE, TWO, THREE, FOUR.

Vanessa says, AWESOME. NEXT ROLL.

Vanessa rolls the die and says, A ONE. HOW ABOUT YOU DO

ONE NECK CIRCLE?

Chase and Vanessa do a neck circle.

Vanessa says, NEXT ROLL, WE HAVE

A ONE AGAIN.

HOW ABOUT ONE HIGH KNEE?

Chase raises his left knee.

Vanessa says, OKAY. LAST ROLL.

ARE YOU READY?

Chase says, YEAH.

Vanessa rolls the die and says, SIX. LET'S DO

SIX ARM CIRCLES

TO GET OUR ARMS READY TO

WRITE AND PLAY SOME GAMES.

Chase circles his arms and counts, ONE, TWO, THREE, FOUR,

FIVE, SIX.

Vanessa says, ALL RIGHT. AND LET'S TAKE

SOME BIG, DEEP BREATHS

BEFORE WE BEGIN,

CHASE.

(BOTH INHALING AND EXHALING)

Vanessa says, ONE MORE.

(INHALING AND EXHALING)

Vanessa continues, BREATHE OUT. AND SAY, "BYE

AND THANK YOU" TO EVERYBODY.

Chase waves and says, BYE.

Vanessa says, THANK YOU

FOR JOINING US, CHASE.

An animated sun rises.

Notes on a tabletop display beside Vanessa read, Probability, the likelihood of something happening.

Shown through a fraction and number line. Use probability to make decisions and predictions.

Vanessa says, SO, TODAY, WE'RE GOING TO

TALK ABOUT PROBABILITY,

THE LIKELIHOOD

OF AN EVENT OCCURRING.

HAVE YOU EVER WONDERED

WHAT THE WEATHER PERSON

IS TALKING ABOUT WHEN THEY SAY,

"THERE'S A 50% CHANCE

OF RAIN OR SNOW"?

OR IF YOU HAVE A VERY SMALL

CHANCE OF WINNING THE LOTTERY?

WHAT ARE THEY TALKING ABOUT?

TODAY, I'M GOING TO SHOW YOU

HOW YOU CAN SOLVE

FOR PROBABILITY

USING FRACTIONS

AND A NUMBER LINE.

WE'RE GOING TO USE PROBABILITY

TO MAKE DECISIONS

AND FUTURE PREDICTIONS.

SO, IF YOU HEARD THAT

THERE WAS A SNOWSTORM COMING,

YOU WOULD PRETTY--

YOU'D BE PRETTY WELL

TO BRING SNOW PANTS

AND MITTENS TO SCHOOL THAT DAY,

SO YOU'RE PREPARED FOR

THE WEATHER.

WE'RE GOING TO PLAY SOME

FUN GAMES TODAY WITH SPINNERS,

DICE AND CARDS.

SO, I WOULD LOVE FOR YOU

TO GET THOSE MATERIALS

IF YOU HAVE THEM LAYING AROUND,

OR YOU COULD MAKE

YOUR OWN CARDS.

YOU COULD MAKE YOUR OWN DICE.

I MADE THESE OUT OF

A PIECE OF CARDBOARD.

IT'S VERY SIMPLE. ALL YOU NEED

TO MAKE THE CARDBOARD DIE

ARE TAPE, CARDBOARD AND MARKERS.

IF YOU HAVE SOMETHING LIKE

A LAZY SUSAN LAYING AROUND--

YOUR PARENTS

WILL KNOW WHAT THAT IS--

YOU CAN TAPE SOME PAPER TO IT

AND IT'LL SPIN LIKE A SPINNER,

OKAY?

Vanessa holds up a lazy susan covered with colored paper in white, blue, red and yellow quadrants.

Vanessa says, I USED JUST YOUR RUN-OF-THE-MILL

DECK OF CARDS.

IF YOU HAVE A COIN OR TWO,

WE COULD DO SOME COIN TOSSES

LATER ON.

I'M GOING TO SHOW YOU SOME

REALLY COOL GAMES AND ACTIVITIES

YOU COULD DO WITH YOUR FRIENDS.

BUT BEFORE WE DO, LET'S WATCH

THIS EPISODE OF

LADY VOCAB,

WHO'S GOING TO GO INTO

THE DEFINITION OF PROBABILITY

USING A REALLY COOL SONG.

CHECK IT OUT, AND I'LL CATCH YOU

BACK HERE AFTER.

The animated sun rises.

A title screen reads, The Lady Vocab Show.

Professor P stands in a dark room in front of a monitor ‘with Lady Vocab’ written several times on it.

He wears a black sweater with a large letter P on the front. He has short dark hair and wears glasses.

Professor P says, HEY THERE, WORD FANS,

AND WELCOME TO

THE

LADY VOCAB SHOW.

I'M YOUR HOST,

PROFESSOR P.

AND NOW TO INTRODUCE

THE LONG-WINDED LADY HERSELF,

LADY VOCAB.

Lady Vocab stands behind a microphone.

She has shoulder length blonde hair and wears large sparkling silver glasses, and a black and white costume with the words window, shuttle, machine, and package written on it.

She says, THANKS, PROFESSOR.

ARE YOU READY

TO ROCK THE WORD?

Professor P says, YES, INDEEDY, MILADY.

THE WORD IS "PROBABILITY,"

WHICH IS A TERM THAT MEANS

HOW LIKELY SOMETHING

IS TO HAPPEN.

Lady Vocab says, HIT IT.

(Electronic music plays)

She sings, P-R-O-B-A-B-I-L-I-T-Y

Professor P says, PROBABILITY.

Lady Vocab sings, THE CHANCES THAT

YOU'RE LIKELY TO SUCCEED

JUST USE PROBABILITY

Professor P says, MM-HMM.

Lady Vocab sings, TOSS A COIN, IT'S 50-50

Professor P says, COULD BE HEADS

OR TAILS.

Lady Vocab sings, THE OUTCOME

IS FOR YOU TO SEE

Professor P says, THAT'S RIGHT.

Lady Vocab sings, PROBABILITY

SEEMS LIKELY

Professor P says, MM-HMM.

COULD BE.

Lady Vocab sings, PROBABILITY

CHANCES MAKE YOU LUCKY

Professor P says, HOW LIKELY?

Lady Vocab sings, PROBABILITY.

Professor P says, HMM. WELL, THERE YOU HAVE IT.

THE LIKELIHOOD THAT

I'LL SEE YOU NEXT TIME?

100%, WORD FANS. BYE FOR NOW.

Lady Vocab sings, PROBABILITY

YOU'RE SO LUCKY, PROBABILITY

A red logo over a black background reads, TVO kids. Copyright, The Ontario Educational Commissions Authority MMXIV

The animated sun rises.

Vanessa says, WELCOME BACK.

SO, TODAY WE'RE GOING TO TALK

ABOUT THEORETICAL PROBABILITY.

The caption reads, Junior 4-6. Teacher Vanessa.

A formula written on the tabletop display reads, theoretical probability equals number of favorable outcomes divided by number of possible outcomes.

Vanessa continues, WHAT DOES THAT MEAN?

WHAT ARE YOUR ODDS OF WINNING

WHEN YOU PLAY A GAME?

WHAT ARE YOUR ODDS

OF ROLLING ANY NUMBER ON A DICE?

Vanessa holds up a die.

She continues, WHAT ARE THE ODDS OF GETTING

A HEADS OR TAILS

WHEN YOU FLIP A COIN?

Vanessa holds up a coin.

She continues, AND IF YOU WANTED TO PLAY A GAME

WITH YOUR FRIENDS,

WHAT ARE THE ODDS OF PICKING UP

AN EIGHT IN CRAZY EIGHTS?

LET'S FIGURE THIS OUT.

SO, THEORETICAL PROBABILITY,

OR PROBABILITY,

IS KNOWN AS THE NUMBER

OF FAVOURABLE OUTCOMES

OVER, OR DIVIDED BY

IN A FRACTION FORM,

THE NUMBER OF POSSIBLE OUTCOMES.

SO, WHAT DOES THAT MEAN?

LET'S SAY I HAVE A DICE.

WE KNOW THAT THERE ARE SIX SIDES

TO A DICE,

AND EVERY SIDE HAS A NUMBER

RANGING FROM ONE TO SIX.

Vanessa rolls the die and says, SO, IF I WERE TO ROLL THIS DICE

AND I GET THE NUMBER SIX,

TECHNICALLY I HAVE

A ONE-OUT-OF-SIX PROBABILITY

OF GETTING ANY NUMBER

ON THIS DICE.

IN THIS CASE, I DID ROLL A SIX.

OKAY?

SO, LET'S SAY

I SAID TO MY FRIEND,

"IF I ROLL A FIVE,

I WIN THE GAME."

WHAT ARE MY ODDS OF WINNING?

I KNOW THAT I HAVE TO ROLL

JUST A FIVE,

SO THAT WOULD JUST BE A ONE,

LIKE WE HAVE HERE.

Vanessa holds up a blue card with the fraction 1/6 written on it.

She says, AND THERE ARE

SIX POSSIBLE OUTCOMES

'CAUSE THERE ARE SIX NUMBERS

ON A DICE.

SO, I HAVE A ONE-IN-SIX ODD

OF WINNING THE GAME.

LET'S SEE IF I DID WIN.

Vanessa rolls the die.

She says, NO. I ROLLED A FOUR.

SO UNFORTUNATELY,

MY FRIEND WON THAT ROUND.

FORTUNATELY FOR HER.

OKAY?

Vanessa removes the formula from the display, then picks up the lazy Susan spinner.

She says, LET'S TRY PLAYING WITH

OUR SPINNER.

AND WE HAVE

ONE, TWO, THREE, FOUR

DIFFERENT-COLOURED SECTIONS.

THAT MEANS THE SPINNER

CAN LAND ON

ANY ONE OF THE FOUR SECTIONS.

SO, MY POSSIBILITY--

PROBABILITY OF LANDING

ON THE WHITE, FOR EXAMPLE,

IS ONE OVER FOUR.

MY PROBABILITY OF LANDING

ON THE BLUE

IS ONE OUT OF THE TOTAL OF FOUR

DIFFERENT OPTIONS THERE ARE.

SO, YOU MIGHT SAY

TO YOUR FRIEND,

"IF I LAND ON RED, I WIN,

"BUT IF YOU LAND--

WHEN YOU SPIN AND YOU LAND

ON BLUE, YOU WIN."

SO, LET'S JUST SAY-- LET'S TRY.

I'M GOING TO SAY IF I LAND

ON RED, I GET ONE POINT.

Vanessa spins the spinner and says,

SO, I HAVE MY SPINNER.

I'M GOING TO TURN IT AROUND

AND UNFORTUNATELY,

I LANDED ON--

OH, WAIT, (UNCLEAR).

OH, NO. I LANDED ON THE WHITE.

SO, I DIDN'T GET A POINT, OKAY?

SO, LET'S SAY

IT'S MY FRIEND'S TURN.

AND THIS IS HARDER THAN IT SEEMS

TO HOLD.

(LAUGHING)

Vanessa spins the spinner and says,

AND IT LANDS ON BLUE,

BUT SHE NEEDED RED TO WIN.

SHE DOESN'T WIN.

SO, EITHER WAY, ONE OF US--

OR EACH OF US, I SHOULD SAY,

HAS A ONE-IN-FOUR CHANCE

OF WINNING THAT GAME.

IF I SAID I NEED TO LAND

ON RED

OR

BLUE TO WIN,

WHAT IS MY POSSIBILITY NOW,

MY PROBABILITY OF WINNING?

WE HAVE ONE-HALF.

WHY IS THAT ONE-HALF?

BECAUSE I COULD WIN ONE, TWO

OF A POSSIBLE

ONE, TWO, THREE, FOUR.

SO, TWO OUT OF FOUR

IS THE SAME AS

HAVING THE ODDS

OF HAVING ONE-HALF.

Vanessa holds up a blue card with the fraction 1/2 on it.

She says, SO, PLOTTING THIS

ON A NUMBER LINE,

I'M GOING TO SHOW YOU

SOME TERMS...

Vanessa picks up a long brown sheet of paper with a number line drawn on it.

Notes on the line from left to right read, impossible, unlikely, equally likely, likely, and certain.

The number 0 is at the left end. The number 1 is at the right.

Vanessa continues, ...THAT YOU ARE GOING TO BE

USING

IN MATHEMATICS FOR PROBABILITY.

I LOVE THE NUMBER LINE.

SO, IN THIS CASE

FOR PROBABILITY,

WE HAVE "UNLIKELY"

AND "IMPOSSIBLE"

STARTING AT THE ZERO.

SO, FOR EXAMPLE, YOUR ODDS

OF WINNING THE LOTTERY

ARE VERY, VERY UNLIKELY.

NOT IMPOSSIBLE,

'CAUSE "IMPOSSIBLE" MEANS

IT COULD NEVER HAPPEN.

BUT SOMEWHERE IN THE REALM OF

UNLIKELY TO IMPOSSIBLE.

SO, "IMPOSSIBLE" COULD BE

"THE SUN WON'T RISE TOMORROW,"

WHEN WE KNOW THAT CERTAINLY,

THE SUN WILL RISE EVERY DAY.

SO, WE'RE GOING TO MOVE

FROM IMPOSSIBLE TO UNLIKELY.

LIKE WE SAID,

WINNING THE LOTTERY,

LIKE WE SAID, SPINNING, UM,

MAYBE A WHEEL THAT HAD

A HUNDRED NUMBERS ON IT

AND YOU HAVE TO GET

ONE OF THE NUMBERS.

IT'S VERY UNLIKELY THAT

THE WHEEL WILL SPIN

ON YOUR NUMBER,

FROM ONE OUT OF A HUNDRED.

OKAY? AGAIN, NOT IMPOSSIBLE,

'CAUSE IT MIGHT HAPPEN.

BUT IT COULD BE UNLIKELY.

"EQUALLY LIKELY" MEANS

SOMETHING WILL HAPPEN

AS LIKELY AS IT WILL NOT HAPPEN.

SO, IF I PICK UP A COIN,

FOR EXAMPLE,

I KNOW THAT IT HAS A HEAD

AND A TAIL.

AND BECAUSE THERE'S

ONLY TWO OPTIONS, AGAIN,

I HAVE A ONE-OUT-OF-TWO ODD

OR PROBABILITY

THAT I WOULD ROLL-- OR, SORRY.

FLIP A COIN

AND LAND ON A HEAD.

I HAVE A ONE-IN-TWO PROBABILITY,

THEN,

THAT IT WOULD ALSO--

IT WOULD LAND ON A TAIL.

OKAY? SO, WHEN SOMETHING

IS EQUALLY LIKELY TO HAPPEN

AS IT'S

NOT LIKELY TO HAPPEN,

YOU HAVE A 50-50 CHANCE,

A ONE-OUT-OF-TWO SHOT,

IT IS EQUALLY LIKELY.

A yellow star is in the middle of the number line over the number 0.5.

Vanessa says, UM, SO, FOR SOMETHING TO BE

LIKELY TO HAPPEN,

WE CAN TALK ABOUT SOMETHING LIKE

IF THE WEATHER PERSON SAYS

THERE'S A 75% CHANCE

OF RAIN TODAY,

THAT IS LIKELY

THAT IT WILL HAPPEN.

HOW DO WE KNOW? WE KNEW THAT

SOMETHING CLOSER TO ONE

IS ABSOLUTELY CERTAIN TO HAPPEN.

SO, FOR EXAMPLE,

IF WE SAID YOU HAVE, UM--

IF YOU SPUN A WHEEL

AND IF YOU GOT ANY OF

THE THREE COLOURS EXCEPT WHITE,

YOU WIN, THAT IS LIKELY

THAT YOU WILL WIN THAT GAME,

BECAUSE YOU COULD LAND

ON YELLOW, RED, BLUE,

AND STILL WIN.

THE ONLY WAY YOU WOULD LOSE IS

IF YOU LANDED ON WHITE.

SO, THAT IS

A LIKELY PROBABILITY

THAT YOU WILL WIN.

SOMETHING CERTAIN IS THAT

YOU WILL TURN PLUS-ONE

ON YOUR NEXT BIRTHDAY.

SO, IF YOU ARE NINE, ON YOUR

NEXT BIRTHDAY YOU WILL TURN 10.

IF YOU'RE 10,

ON YOUR NEXT BIRTHDAY

YOU WILL CERTAINLY TURN 11.

YOU ARE AN AWESOME PERSON.

THAT IS CERTAIN.

SO, THAT'S 100% POSSIBILITY.

YOU'RE GREAT AT MATH?

100% POSSIBILITY. TRUST ME.

OKAY? SO, WE HAVE THE RANGE OF

SOMETHING IMPOSSIBLE HAPPENING,

OKAY?

SO AGAIN, WE SAID THAT

UNFORTUNATELY,

IF YOU THOUGHT THAT

THE SUN WILL NOT RISE TOMORROW,

IMPOSSIBLE.

YOU MIGHT WIN THE LOTTERY?

SOMEWHERE IN THE REALM

OF UNLIKELY AND IMPOSSIBLE.

SO, EVERY DAY, WHEN YOU BUY

YOUR LOTTERY TICKET,

AND YOU HAVE A 1 IN 33,000,000

CHANCE OF WINNING,

UNFORTUNATELY THE ODDS ARE

VERY, VERY LOW THAT YOU WIN,

BUT THEY'RE NOT IMPOSSIBLE.

SO, WE HAVE

"WINNING THE LOTTERY"

WOULD BE SOMEWHERE POSSIBLY

CLOSER TO THE ZERO HERE.

BUT DON'T GIVE UP HOPE, FRIENDS,

AS YOU GET OLDER.

(LAUGHING)

AGAIN, "EQUALLY LIKELY,"

WE'RE TALKING ABOUT

FLIPPING A COIN

AND THERE'S ONLY TWO OPTIONS.

(CLEARING THROAT)

WE'RE

TALKING ABOUT PLAYING CARDS,

WHEN YOU ONLY HAVE

RED OR BLACK SUITS.

Vanessa holds up two playing cards.

She continues, YOU'RE EQUALLY LIKELY

TO PICK UP A RED CARD

AS YOU ARE A BLACK CARD.

WE HAVE SOMETHING "LIKELY"

AS 75%,

OR THREE OVER FOUR.

WE TALKED ABOUT THE SPINNER.

WE SAID YOU WON--

WHEN THE GAME IS YOU CHOOSE

RED, YELLOW OR BLUE

OUT OF A TOTAL OF FOUR OPTIONS,

IT'S LIKELY THAT YOU WILL WIN.

AND THEN "CERTAIN," WE TALKED

ABOUT YOU GETTING A YEAR OLDER

FOR YOUR AGE NEXT YEAR, AND FOR

THE SUN SETTING THE NEXT DAY.

SO, WHEN YOU'RE WATCHING TV

AND MAYBE YOU'RE CATCHING

YOUR PARENTS WATCHING THE NEWS,

AND THE WEATHER PERSON SAYS,

"THERE'S A 10% CHANCE

OF PRECIPITATION TONIGHT,"

Vanessa holds a sheet of paper that reads, unlikely, 10%, 1/10, 0.1.

She continues, OKAY, THAT MEANS THAT

THERE'S A ONE-IN-10 CHANCE

OF IT RAINING TONIGHT.

THIS IS EQUIVALENT, MEANING

THAT IT'S THE SAME THING,

WHICH ALSO IS EQUIVALENT TO

ONE-TENTH OUT OF ONE,

FROM ZERO TO ONE.

SO, AGAIN, VERY, VERY UNLIKELY

THAT THIS WOULD HAPPEN.

OKAY? VERY UNLIKELY

FOR THERE TO BE RAIN TODAY.

Vanessa holds a sheet of paper that reads, equally likely, 50%, 5/10, 0.5.

She says, SIMILARLY,

IF SHE SAYS THERE'S A 50--

HE OR SHE SAYS THERE'S

A 50% CHANCE OF RAIN TODAY,

WE KNOW THAT

THAT'S EQUALLY LIKELY.

IT MIGHT RAIN

AS MUCH AS IT MIGHT NOT RAIN.

OKAY? SO, IN THIS CASE,

BETTER TO BE SAFE THAN SORRY.

I WOULD BRING AN UMBRELLA

OR A RAIN JACKET,

WHEREVER YOU'RE GOING.

Vanessa holds a sheet of paper that reads, certain, 90%, 9/10, 0.9.

Vanessa continues, AND IF SHE SAID--

OR HE SAID, I SHOULD SAY--

A 90% CHANCE OF RAIN TODAY,

IT'S ALMOST CERTAIN

THAT IT'S GOING TO RAIN.

SO, IN THIS CASE,

I WOULD USE THIS PROBABILITY

TO MAKE A DECISION

AND BRING AN UMBRELLA,

RAIN JACKET, RAIN BOOTS

TO SCHOOL

OR WHEREVER YOU'RE GOING TO PLAY

THAT DAY.

SO, YOU SEE

Vanessa holds up the number line and continues,

FROM OUR NUMBER LINE

THAT PROBABILITY RANGES

FROM ZERO, WHICH MEANS,

WHICH IS-- SORRY--

EXTREMELY UNLIKELY, IMPOSSIBLE.

TO ONE, WHICH IS MEANING

CERTAINLY SOMETHING WILL HAPPEN.

OKAY?

SO, IN THE NEXT SEGMENT,

WHEN WE TALK ABOUT

DIFFERENT GAMES,

WE'RE GOING TO PLOT THIS

AND DIFFERENT SCENARIOS

THAT YOU MIGHT DEAL WITH

ON A DAILY BASIS

ON OUR NUMBER LINE.

LET'S PLAY ONE MORE GAME

BEFORE WE WATCH OUR NEXT SHOW.

I HAVE A DECK OF CARDS HERE.

AND THEY RANGE FROM ACE

ALL THE WAY UP TO 10, AND

THEN WE HAVE THREE FACE CARDS

WITH THE ACE.

SORRY. THREE FACE CARDS.

SO, EACH SUIT HAS 13 CARDS.

WE HAVE THE HEARTS,

THE DIAMONDS, THE SPADES

AND THE CLUBS.

Vanessa shuffles a deck of cards and says,

IF I SAID TO YOU, "WHAT ARE

THE ODDS OF PICKING UP

A SUIT OF HEARTS

OUT OF MY DECK,"

WHAT WOULD THE ODDS BE?

Vanessa puts the formula back onto the display and says,

KNOWING THAT OUR

THEORETICAL PROBABILITY, AGAIN,

IS THE NUMBER

OF FAVOURABLE OUTCOMES--

SO, WE KNOW THAT THERE ARE

13 HEARTS IN OUR DECK.

OVER HOW MANY TOTAL

OR POSSIBLE OUTCOMES ARE THERE.

WE KNOW THAT THERE ARE 52 CARDS

IN THE DECK.

SO, 13 OVER 52

IS OUR FRACTION THAT WE USE,

Vanessa holds up a blue card with the fraction 13/52 on it.

She continues, WHICH IS THE SAME THING

AS ONE OVER FOUR.

SO, WE HAVE

A ONE-OUT-OF-FOUR CHANCE

OF PICKING UP A HEART WHEN I...

...QUICKLY SHUFFLE.

AND I'M GOING TO PICK

THE FIRST CARD ON TOP.

SO, I HAVE

A ONE-OUT-OF-FOUR CHANCE,

WHICH UNFORTUNATELY IS UNLIKELY.

OR MAYBE YOU DON'T WANT

TO PICK A HEART.

THAT'S YOUR FAVOURITE SUIT.

BUT LET'S SAY IT'S UNLIKELY

THAT YOU'RE GOING TO PICK

A HEART, A CARD THAT HAS

THE SUIT OF A HEART IN IT.

COMPARED TO--

THERE'S STILL CLUBS.

THERE'S STILL SPADES.

AND THERE'S STILL DIAMONDS.

SO, YOU'RE MORE LIKELY TO PICK

ONE OF THE OTHER THREE SUITS

THAT ARE REMAINING.

SO, ARE YOU READY TO SEE

IF I CAN PICK A HEART?

Vanessa draws the ace of hearts out of the deck of cards.

She says, OH, MY GOODNESS!

I DID.

(LAUGHING)

OKAY. SO, EVEN THOUGH MY ODDS

WERE UNLIKELY

THAT I WOULD PICK THIS,

ONE OUT OF FOUR,

I WAS STILL ABLE TO DO IT.

SO, THERE'S STILL HOPE OUT THERE

FOR ALL OUR LOTTERY PLAYERS.

ANYWAYS, I WOULD LIKE NOW

JUST TO THROW TO HAMZA,

AND HE IS FROM THE SHOW

LOOK KOOL,

AND HE'S GOING TO GO THROUGH

SOME AWESOME PROBABILITY GAMES,

EXPERIMENTS AND DEFINITIONS

OVER THE COURSE OF

A FEW MINUTES.

I HOPE YOU REALLY ENJOY,

AND I'LL SEE

ALL YOU PROBABILITY LOVERS

HERE AFTER THE VIDEO.

The animated sun rises.

Hamza flips a coin. He is clean shaven with short dark hair.

He wears a navy blue dress shirt and an orange and white striped bow tie.

Hamza says, OKAY.

HEADS.

TAILS? LET'S TRY IT AGAIN.

TAILS.

HEADS?

WHAT ARE THE ODDS I'M EVER

GOING TO GET THIS RIGHT?

TO FIND OUT,

WE'LL MEET A BIG CARD...

A man wearing Jack of Hearts costume enters the room.

(IN FRENCH ACCENT)

The man says, I AM JACQUES DESCARTES.

Hamza says, YEAH. YOU'RE THE ONE I NEEDED

TO WIN GO FISH YESTERDAY.

A clip plays.

...LAUNCH POWERFUL ROCKETS

YOU CAN BUILD AT HOME...

WHOA!

...AND DISCOVER AN UNBELIEVABLE

SCIENTIFIC FACT...

A young girl kneels and puts a microphone to a small white dog’s face.

She says, WHEN'S YOUR BIRTHDAY?

MINE IS NOVEMBER 9TH.

OH. WE HAVE A MATCH.

Hamza says, ...ON

LOOK KOOL.

(Upbeat music plays)

Hamza spins and puts on sunglasses. He wears a blue shirt and a white and blue striped bow tie.

Colorful geometric shapes fall onto a grassy field. The shapes grow to form a colorful city skyline.

(KOOL KATT MEOWING)

Colorful bridges form over a river. A yellow staircase rotates around a red tower.

A purple airplane circles the tower. Koolkatt watches an orange tower rise from the ground.

The title, Look Kool appears over a blue sky.

A coin shoots out of KoolKatt’s toaster-shaped back.

Hamza catches it and says, HEADS.

TAILS AGAIN.

HOW IS THIS POSSIBLE?

THAT'S, LIKE, 10 IN A ROW NOW.

KOOL CAT AND I

ARE PLAYING FLIP THE COIN.

AND SO FAR, HE'S WON EVERY TIME.

(LAUGHING)

MAYBE I NEED SOME OLD FASHIONED

LUCKY CHARMS,

LIKE THIS FOUR-LEAF CLOVER

AND THIS HORSESHOE.

OKAY, OKAY. ONE MORE.

ONE MORE. LET'S GO.

KoolKatt shoots out another coin.

Hamza catches it and says, HEADS.

TAILS AGAIN.

HOW IS THIS POSSIBLE?

THAT'S, LIKE, 10 IN A ROW NOW.

IT LOOKS LIKE

YOU COULD USE SOME HELP.

WHO ARE YOU?

Jacques enters the room.

He says, I AM JACQUES DESCARTES.

PERHAPS YOU REMEMBER ME

FROM YOUR DECK OF CARDS, NO?

Hamza says, YEAH. YOU'RE THE ONE I NEEDED

TO WIN GO FISH YESTERDAY.

NOW YOU DECIDE TO SHOW UP?

Jacques says, AND DO NOT BLAME ME

FOR PROBABILITY.

I DO NOT MAKE THE RULES.

Hamza says, PROBABILITY? WHAT'S THAT?

Jacques says, PROBABILITY IS A TYPE OF MATH

THAT HELPS PREDICT HOW LIKELY

SOMETHING IS TO HAPPEN.

Hamza says, WAIT. YOU MEAN MATH

CAN TELL ME HOW LIKELY IT IS

I'LL GET THE CARD I NEED

IN GO FISH,

OR WIN A COIN TOSS?

Jacques says, UH, YES.

I MEAN, WE CARDS KNOW ABOUT IT,

BUT WE PLAY

GAMES OF CHANCE ALL DAY LONG.

Hamza says, CAN YOU TELL ME

WHY KOOL CAT KEEPS WINNING?

Jacques says, I KNOW EXACTLY WHY KOOL CAT

KEEPS WINNING.

AND MAYBE YOU'LL FIGURE

THAT OUT FOR YOURSELF, EH?

(SNORTING ARROGANTLY)

KoolKatt shakes his head.

Hamza says, OKAY. CAN YOU TELL ME

HOW PROBABILITY WORKS?

Jacques says, OF COURSE.

PROBABILITY IS

THE NUMBER OF OUTCOMES YOU WANT

DIVIDED BY THE NUMBER

OF POSSIBLE OUTCOMES.

Hamza says, OH, OKAY.

SO, I WANT HEADS, AND THERE'S

ONLY TWO POSSIBLE OUTCOMES,

HEADS OR TAILS.

SO, THAT'S ONE DIVIDED BY TWO,

WHICH IS THE SAME AS ONE-HALF.

SO, TECHNICALLY, IT SHOULD BE

ON HEADS HALF THE TIME, RIGHT?

Jacques says, YOU'RE RIGHT.

IT SHOULD.

BUT EVEN WITH MY LUCKY

FOUR-LEAF CLOVER AND HORSESHOE,

KOOL CAT KEEPS WINNING.

Jacques snorts and says, LUCK HAS NOTHING TO DO WITH IT.

An animated 4-leaf clover walks through a field of clovers and says, OH, BOY. I FEEL LUCKY TODAY.

A brown shoe steps on the clover. The clover sticks to the bottom of the shoe, then frees itself.

The clover says, OOH. I SHOULD HAVE BROUGHT

MY LUCKY HORSESHOE.

A horseshoe falls on the clover.

The clover says, OH, MAN.

Hamza says, CAN YOU USE PROBABILITY

TO PREDICT

ANYTHING

OTHER THAN GAMES?

Jacques says, UH, YES, ABSOLUTELY.

I MEAN, PROBABILITY CAN TELL YOU

HOW LIKELY IT IS

THAT YOU'LL FIND A PEARL

IN AN OYSTER.

An animated oyster opens. A pearl is inside it.

Jacques continues, ONE IN 12,000.

OR HOW LIKELY IT IS THAT

A FAMILY WILL HAVE TRIPLETS.

ONE IN 44,000.

A picture of triplets appears.

Jacques continues, OR IT CAN TELL YOU

HOW LIKELY IT IS

THAT A GROWN-UP PERSON

WILL GO TO THE EMERGENCY ROOM

WITH A POGO STICK INJURY.

ONE IN 115,300.

A man hops on a pogo stick, then crashes.

The man says, OW!

Hamza says, SO, PROBABILITY IS AN

EXACT WAY TO LOOK AT THINGS?

Jacques says, UH, IT'S NOT EXACT.

BUT IT DOES SHOW YOU

HOW LIKELY OR UNLIKELY

IT IS TO HAPPEN.

Hamza says, OH, YEAH.

I MEAN, IF SOMETHING'S UNLIKELY,

THAT DOESN'T MEAN

THAT IT'S IMPOSSIBLE.

I MEAN, UNLIKELY THINGS

HAPPEN ALL THE TIME.

(Upbeat woodwind and tuba music plays)

Hamza flies through the sky wearing a pig costume. He flies in formation with several animated pigs.

He sings, NOT UNTIL PIGS FLY

THAT'S WHAT THEY SAY

WHEN SOMETHING'S UNLIKELY

BUT I'M HERE TODAY

FLAPPING MY WINGS

ON THE WAY TO THE SUN

THE ODDS WERE

200 TRILLION BILLION TO ONE

BUT JUST 'CAUSE IT'S RARE

DOESN'T MEAN IT'S NOT DONE

I SAID JUST 'CAUSE IT'S RARE

DOESN'T MEAN IT'S NOT DONE

OINK-OINK-OINK, OINK-OINK-OINK

OINK-OINK-OINK

SOMETIMES A RIVER

IS BACKWARDS FLOWING

SOMETIMES

A TURTLE IS NOT SO SLOWING

SOMETIMES IN SUMMER

IT STARTS SNOWING

AND NOW THAT

YOU'RE ALL KNOWING

I REALLY MUST BE GOING

OINK-OINK-OINK, OINK-OINK-OINK

OINK-OINK-OINK

Hamza says, SO, DO YOU THINK

KOOL KATT WINNING

10 TIMES IN A ROW

IS JUST PURE LUCK?

Jacques says, HA! I THINK

THAT'S AWFULLY IMPROBABLE.

Hamza says, YEAH. ME, TOO.

SO, WHAT ELSE CAN YOU TELL ME

ABOUT PROBABILITY?

Jacques says, OH, HERE IS ONE OF

MY FAVOURITE THINGS.

A graphic appears showing 23 human figures.

Jacques continues, IF YOU HAVE A ROOM OF 23 PEOPLE,

THERE IS A ONE IN TWO CHANCE

THAT TWO OF THEM

WILL HAVE THE SAME BIRTHDAY.

A box appears around two figures.

Hamza says, NOW, THAT DOESN'T

SOUND RIGHT.

I MEAN, THERE'S 23 PEOPLE

AND 365 DAYS IN A YEAR.

Jacques says, I DEAL IN PROBABILITY.

I KNOW WHAT I AM TALKING ABOUT.

Hamza says, OKAY, OKAY.

NO OFFENCE, MONSIEUR.

BUT I THINK I'M GOING TO

HAVE THE INVESTIGATORS

CHECK THIS OUT.

Jacques says, WELL, SUIT YOURSELF.

An animated KoolKatt looks through a magnifying glass.

An announcer says, INVESTIGATION.

A young boy and girl appear on a screen.

Hamza says, HI, INVESTIGATORS.

The kids say, HI, HAMZA.

Hamza says, ALEXANDRA, ETHAN,

I HAVE A QUESTION FOR YOU.

A TYPICAL YEAR

HAS 365 DAYS, RIGHT?

Alexandra and Ethan say, YEAH.

RIGHT.

Hamza says, SO, HOW MANY DIFFERENT

BIRTHDAY DATES

COULD THERE BE IN THE YEAR?

Alexandra and Ethan say, 365?

Hamza says, EXACTLY. SO, HOW MANY

PEOPLE DO YOU THINK

YOU'D HAVE TO ASK

BEFORE YOU'D FIND TWO

WITH THE SAME BIRTHDAY?

Alexandra says, WELL, I THINK WE SHOULD

DIVIDE IT IN TWO,

'CAUSE WE NEED

TWO PERSONS.

Ethan says, OR 185?

Alexandra says, YEAH, ABOUT THAT.

Hamza says, YOU KNOW, I THINK IT

WOULD TAKE A LOT OF PEOPLE, TOO.

BUT I HAVE A BUDDY HERE WHO

THINKS YOU'D NEED A LOT LESS.

LET'S TEST IT.

ASK PEOPLE THEIR BIRTHDAYS

UNTIL YOU FIND A MATCH.

Ethan says, WE'RE ON IT.

The kids approach a group of people outside a large grey brick and stone building.

Ethan says, WE'RE DOING A TV SHOW

ON PROBABILITY,

AND WE'RE WONDERING

WHAT YOUR BIRTHDAY IS.

A woman says, THE 14TH OF FEBRUARY.

Alexandra asks, AND WHAT'S

YOUR BIRTHDAY?

A woman says, MARCH 24TH.

Alexandra kneels beside the small white dog and holds a microphone to its face. She asks, WHEN'S YOUR BIRTHDAY?

COME ON, TELL ME.

The dog’s male owner says, HE ONLY

SPEAKS FRENCH.

Alexandra says, OH.

A line graph appears.

A computerized voice says,

ACCORDING TO THE LAWS

OF PROBABILITY,

IN A ROOM WITH 23 PEOPLE,

IT'S MORE THAN 50% CERTAIN

THAT AT LEAST TWO

WILL HAVE THE SAME BIRTHDAY.

WITH 30 PEOPLE IT'S 75%,

AND WITH 70 IT'S 99%.

BY DOING LOTS OF EXPERIMENTS

LIKE THESE,

WE CAN SEE THAT THE LAWS

OF PROBABILITY WORK.

Ethan holds a microphone up to a woman and asks, AND YOU?

The woman says, MAY THE 18TH.

Several women answer Alexandra and Ethan, MAY 26TH.

SEPTEMBER 6TH.

FEBRUARY 22ND.

AUGUST 28TH.

MAY THE 18TH.

Ethan says, WE GOT TWO.

Hamza says, WOW!

Alexandra says, ALL RIGHT.

THANK YOU.

Hamza asks, HOW MANY DID IT TAKE?

Alexandra counts checkmarks on a grid and counts, ONE, TWO, THREE,

FOUR, FIVE, SIX,

SEVEN, EIGHT, NINE,

10, 11, 12, 13.

Ethan says, JUST 13.

Alexandra says, YEAH. A LOT LESS

THAN WE THOUGHT.

Hamza says, THAT'S A LOT LESS

THAN WE BOTH THOUGHT.

WE'LL CATCH UP

WITH THE INVESTIGATORS LATER.

BUT THE PROBABILITY THAT

I'M BLOWN AWAY BY THIS IS 100%.

Jacques says, AHA!

I KNEW HE'D SEE IT MY WAY.

Hamza continues, PROBABILITY SAYS THAT

A COIN SHOULD LAND HEADS

HALF THE TIME, RIGHT?

SO, MAYBE

I'LL JUST STICK TO HEADS,

AND MAYBE KOOL CAT'S COIN

WILL LAND ON HEADS

A BUNCH OF TIMES IN A ROW.

Koolkatt shakes his head.

Jacques says, AH, EXCUSEZ-MOI.

HOLD YOUR HORSES.

UH, YOU'VE FALLEN FOR

THE MONTE CARLO FALLACY.

Jacques plays Go Fish with KoolKatt.

Jacques says, UH--

GO FISH.

Hamza says, THE MONTE CARLO

WHAT-ACY?

Jacques says, FALLACY. IT'S WHEN

SOMETHING IS NOT TRUE.

IN THIS PARTICULAR CASE,

IT IS THE IDEA THAT

IF YOU'VE HAD BAD LUCK,

YOUR LUCK

HAS TO CHANGE.

THE PROBABILITY OF FLIPPING

A COIN TO TAILS 10 TIMES IS--

IT'S SMALL.

BUT THE PROBABILITY

OF EACH INDIVIDUAL FLIP

IS THE EXACT SAME

EVERY TIME YOU FLIP IT.

DO YOU HAVE ANY THREES?

Koolkatt shakes his head.

Hamza says, I GUESS I STILL HAVE A LOT MORE

TO LEARN ABOUT PROBABILITY.

(Upbeat music plays)

Panels of a puzzle shift and become a picture of Koolkat.

A graphic of a cat head with ears inside it appears.

An announcer says, BRAIN BENDER

Hamza says, TODAY'S PUZZLE-SOLVERS

ARE EVAN AND ALYSSA.

HELLO.

Evan and Alyssa wave and say HI, HAMZA.

HI.

Hamza says, OUR BRAIN-BENDER

IS GOING TO BE A BIT DICEY.

YOU SEE A PAIR OF DICE,

RIGHT?

The kids say, YEAH.

Hamza says, THERE ARE 12 CUPS.

EACH CUP REPRESENTS A NUMBER YOU

COULD ROLL WITH A PAIR OF DICE.

HERE'S THE BRAIN-BENDER.

IF YOU ROLL A PAIR OF DICE

A LOT OF TIMES,

WHICH OF THESE 12 NUMBERS

DO YOU THINK

YOU'LL GET MOST OFTEN?

Evan says, FIVE. FOUR, MAYBE.

Hamza says, WELL,

LET'S FIND OUT.

Evan rolls the dice and says, FOUR.

He drops a token into a red and white cup labelled with the number 4.

Alyssa rolls the dice and says, SIX.

She drops a token into a cup labelled with the number 6.

Evan rolls the dice and says, SEVEN. THERE.

Alyssa rolls the dice and says, 10.

She rolls again and says, SEVEN.

SIX AND SEVENS

ARE IN THE LEAD.

The kids roll the dice repeatedly.

Hamza says, IT LOOKS LIKE THEY'RE ON A ROLL.

WE'LL CHECK BACK WITH THEM

LATER.

(BRAKES SQUEALING)

An animation shows blue and yellow KoolKatts racing down a street.

The announcer says, CHALLENGE.

Hamza stands in a park with two teams of one boy and one girl wearing yellow or blue shirts.

He says, WELCOME TO THE

LOOK KOOL

PROBABILITY CARNIVAL.

AND TO MY RIGHT, I HAVE KIKI

AND ZACHARY. TEAM YELLOW.

Kiki and Zacahry say, TEAM YELLOW.

Hamza continues, AND ON MY LEFT, I HAVE

ELENI AND DONATO. TEAM BLUE.

Eleni adn Donato says, TEAM BLUE.

Hamza and the kids approach a game with several picture of KoolKatt wearing a clown hat and nose.

Hamza says, FIRST UP, WE HAVE

THE BALL TOSS.

BUT BE WARNED.

ONE OF THESE CLOWNS

IS THE DREADED CLOWN OF DOOM.

A red mannequin head wears a colorful clown wig.

(EVERYONE GASPING)

Hamza says, MM-HMM. WHOEVER KNOCKS IT OVER

WILL FACE DIRE CONSEQUENCES.

ZACHARY, YOU GET TO GO FIRST.

He throws a ball through one of the KoolKatt pictures. Text over the clown head reads, safe.

Hamza says, OOH. LET'S TAKE A CLOSER LOOK AT

THIS WITH MY MIND'S EYEGLASSES.

Hamza puts on glasses.

A computerized voice says,

NOW THAT ONE OF

THE EIGHT CLOWNS

HAS BEEN ELIMINATED,

THE PROBABILITY OF HITTING

THE CLOWN OF DOOM

BECOMES ONE IN SEVEN.

Hamza removes the glasses and says, WHOA!

NOW IT'S TEAM BLUE'S TURN.

Kids take turns throwing balls at the wall of KoolKatt pictures.

Hamza says, YES.

WOO-HOO-HOO!

The computerized voice says, WITH EVERY SAFE SHOT,

THE DANGER INCREASES.

THE PROBABILITY

IS NOW ONE IN FIVE.

ALL RIGHT, DONATO.

Kids take turns throwing balls at the wall of KoolKatt pictures.

Hamza says, OOH.

KEANA, THE PROBABILITY IS?

Keana says, ONE OUT OF TWO.

Hamza says, ONE OF THESE IS

THE CLOWN OF DOOM.

LET'S FIND OUT WHICH ONE IT IS.

Keana throws a ball and knocks over a picture.

Hamza says, WOO-HOO-HOO!

DONATO, WHAT DO YOU THINK

IS THE PROBABILITY THAT

THAT IS THE CLOWN OF DOOM?

Donato says, ONE OUT OF ONE.

Hamza says, I'M PRETTY SURE

YOU'RE RIGHT.

Donato throws a ball at the last picture. It flips over revealing a picture of a clown.

(SIREN WAILING)

Hamza says, OH! THERE IT IS.

Donato says, UH-UH.

Water sprays Donato from the mouth of the red mannequin head.

He falls over laughing and says, UGH!

Hamza says, WELL, I THINK THE

PROBABILITY OF THIS CHALLENGE

GETTING WETTER IS REALLY HIGH

WHEN WE GET BACK.

Two red water balloons pop.

(EVERYONE CHEERING)

Hamza flips a coin and says, OH, HEADS. IF IT'S HEADS HALF

THE TIME I FLIP THE COIN,

HOW COME KOOL CAT KEEPS WINNING?

OH, WELL. LET'S SEE HOW

THE BRAIN-BENDER IS GOING.

Hamza approaches the screen and waves his hand.

Evan says, THE LAST ROLL

OF THE GAME IS...

Evan rolls the dice.

Evan and Alyssa say, ...FIVE.

Evan drops a token into a cup

He says, OH.

Hamza says, OKAY. IT'S TIME TO COUNT UP

HOW MANY TOKENS ARE IN EACH CUP.

Evan and Alyssa take tokens out of the cups and count,

12, WE HAVE FOUR.

SIX, 10.

THREE, SEVEN AND EIGHT.

WOW. WE GOT A LOT.

15.

IN SIX WE HAVE 13.

IN FIVE WE HAVE SEVEN.

FOUR, FIVE. SIX.

IN TWO, WE ONLY HAVE ONE.

AND IN ONE, NOTHING.

Evan says, YOU KNOW, IT'S ACTUALLY

IMPOSSIBLE TO GET A ONE,

BECAUSE THERE'S TWO DICE.

Hamza says, SO, TELL ME WHICH ONE

ACTUALLY HAD THE MOST.

The kids say, SEVEN.

Hamza says, DO YOU KNOW WHY?

Evan says, NO.

Hamza says, WHY DO YOU THINK

THEY CALL IT

LUCKY NUMBER SEVEN?

Evan says, MAYBE BECAUSE SEVEN ALWAYS WINS.

Alyssa says, A REALLY GOOD ANSWER,

I THINK.

Hamza says, PROBABLY.

THANKS, EVAN. THANKS, ALYSSA.

Evan and Alyssa wave and say, BYE, HAMZA.

BYE.

Evan rolls two yellow and orange dice and says,

THERE YOU GO. SEVEN.

I'M GOING TO SEE IF THERE'S

A MATHEMATICAL EXPLANATION

BEHIND "LUCKY SEVEN."

IF I HAVE TWO DICE,

HOW MANY DIFFERENT WAYS

CAN I ROLL SEVEN?

The animation of KoolKatt breaks into multiple pieces then reforms whole.

The announcer says, DECONSTRUCT.

Hamza says, DECONSTRUCT.

WHOA.

The dice float in mid air, rotating into various combinations of seven.

Hamza says, ARE YOU SEEING WHAT I'M SEEING?

THERE ARE A LOT OF POSSIBLE

COMBINATIONS TO MAKE SEVEN.

A graphic appears showing all possible dice combinations.

Hamza says, OH, AND LOOK.

THERE'S A PATTERN

TO THE COMBINATIONS.

THERE'S ONE WAY TO MAKE TWO,

TWO WAYS TO MAKE THREE,

THREE WAYS TO MAKE FOUR,

FOUR WAYS TO MAKE FIVE,

FIVE WAYS TO MAKE SIX,

AND SIX WAYS TO MAKE SEVEN.

THE NUMBER OF POSSIBILITIES

INCREASES BY ONE

UNTIL YOU GET

TO SEVEN.

AND THEN IT DECREASES

FOR EVERY NUMBER AFTER THAT

UNTIL YOU GET TO 12.

HEY, IT MAKES A TRIANGLE.

SO, "LUCKY SEVEN"

IS ACTUALLY JUST

THE MOST LIKELY NUMBER

THAT YOU CAN ROLL WITH TWO DICE.

IT'S NOT REALLY LUCK AT ALL.

The 4-leaf clover walks and smiles.

He says, OH, BOY. I FEEL LUCKY TODAY.

UH-OH.

(THUNDER CRASHING)

Rain falls on the clover, then lightning strikes it.

The clover lies on the ground and says, WELL, I GUESS I SHOULDN'T HAVE

CARRIED THIS BIG HUNK OF METAL

IN A THUNDERSTORM.

OH, NO.

Lightning strikes the horseshoe. The horseshoe falls on the clover.

The clover says, OH, MAN.

The animated KoolKatt looks through the magnifying glass.

The announcer says, INVESTIGATION.

A woman says, MY BIRTHDAY IS NOVEMBER 21ST.

Ethan and Alexandra chase after a pigeon.

They yell, WHEN'S YOUR BIRTHDAY?

NO, DON'T GO. WAIT!

A man says, NOVEMBER 16TH.

Ethan says, AND YOU?

Several people respond, NOVEMBER 9TH.

10TH OF MARCH.

22ND OF NOVEMBER.

MINE IS NOVEMBER 9TH.

Alexandra says, OH, WE HAVE A MATCH.

Hamza says, OKAY.

HOW MANY PEOPLE DID IT TAKE

TO GET A BIRTHDAY MATCH

THIS TIME?

Alexandra says, 37.

THAT'S NOT A LOT...

Ethan says, ...COMPARED TO

WHAT WE THOUGHT.

Alexandra says, YEAH. 180 COMPARED TO 37?

THAT'S NOTHING.

Hamza says, NEITHER TRY TOOK 180 PEOPLE.

Ethan and Alexandra say,

NO.

NOT EVEN CLOSE.

The line graph appears.

The computerized voice says, THE PROBABILITY

OF FINDING A MATCH

AFTER ASKING 13 PEOPLE

IS ONLY 19%.

THAT IS SOMEWHAT UNLIKELY.

THE PROBABILITY

OF FINDING A MATCH

AFTER 37 PEOPLE IS 85%.

VERY LIKELY.

AFTER ASKING ONLY 60 PEOPLE,

YOU ARE ALMOST CERTAIN

TO HAVE A MATCH.

Hamza says, THE NUMBER OF PEOPLE

IS A LOT LOWER

THAN WE THOUGHT.

READY TO DO

SOME ROCKET SCIENCE NOW?

Ethan says, YEAH.

Alexandra says, OH, YEAH. BIG TIME.

The animated sun rises.

Vanessa says, WELCOME BACK.

I HOPE YOU ENJOYED THE VIDEO.

The caption reads, Junior 4-6. Teacher Vanessa.

She continues, WE'RE GOING TO TALK ABOUT

THE ODDS

OF MULTIPLE EVENTS HAPPENING.

SO, YOU SEE TO MY RIGHT HERE,

OR YOUR LEFT,

THREE DIFFERENT SPINNERS.

AND WE HAD JUST TALKED ABOUT

THEORETICAL PROBABILITY

BEING THE NUMBER OF

LIKELY EVENTS

OVER THE TOTAL POSSIBILITY

OF EVENTS THAT COULD HAPPEN.

SO, IF WE LOOK FIRST

ON THIS SPINNER,

IF I WANTED TO LAND ON

ONE OF THE SIDES OF THE SPINNER,

I'D HAVE A PROBABILITY

OF ONE OVER TWO.

OKAY? SO, I COULD EITHER LAND

HERE OR I COULD LAND HERE.

Vanessa points at a circle divided into two sections.

She continues, THAT MEANS I HAVE

AN EQUALLY LIKELY PROBABILITY

THAT I'D LAND ON THE BLUE SIDE

Vanessa colors half the circle blue.

COMPARED TO LANDING ON

THE WHITE SIDE.

EQUALLY LIKELY.

IN THE MIDDLE SPINNER, I HAVE

ONE, TWO, THREE, FOUR SECTIONS.

SO, THE ODDS OF ME LANDING ON

ANY ONE OF THOSE FOUR SECTIONS

IS ONE OUT OF FOUR.

AND ON THE SPINNER HERE,

WE SEE THAT WE HAVE

ONE, TWO, THREE, FOUR,

FIVE, SIX.

SO, THE LIKELIHOOD OF ME LANDING

ON ANY ONE OF THOSE SECTIONS

OF THE SPINNER IS ONE OVER SIX.

OKAY? SO, AS YOU SEE,

YOUR ODDS OF LANDING ON

ANY ONE SECTION

GET SMALLER, EVEN THOUGH

THE FRACTION GETS BIGGER.

THE PERCENT GETS SMALLER

AS YOU HAVE MORE SECTIONS ADDED.

Vanessa removes the drawings of circular spinners from the tabletop display.

A new sheet reads, Red twice in a row: 1/4 x 1/4.

Vanessa continues, SO, WHAT HAPPENS IF ONE OF

YOUR FRIENDS AND YOURSELF

PLAY A GAME,

AND YOU ARE SPINNING

A WHEEL,

AND YOU HAVE FOUR SECTIONS.

AND THE WAY TO WIN IS IF

YOU LAND ON RED TWICE IN A ROW.

WHAT ARE YOUR ODDS

OF WINNING THE GAME?

OKAY?

SO, WE KNOW THAT WE HAVE

A ONE-OUT-OF-FOUR PROBABILITY

OF WINNING,

BECAUSE WE KNOW WE HAVE ONE RED

OUT OF A TOTAL OF FOUR.

OKAY? SO, AFTER ONE SPIN,

THAT'S THE PROBABILITY.

WHAT ARE THE ODDS

THAT YOU CAN GET IT TWICE?

SO, ON YOUR SECOND SPIN,

YOU AGAIN HAVE

A ONE-OUT-OF-FOUR PROBABILITY

OF YOU SPINNING A RED.

IN TOTAL,

TO FIND OUT WHAT OUR PROBABILITY

WOULD BE

FOR THESE TWO EVENTS HAPPENING

AFTER EACH OTHER,

WE CAN MULTIPLY

THE TWO FRACTIONS TOGETHER.

SO, WHEN WE MULTIPLY FRACTIONS,

WE LOOK TO MULTIPLY

THE NUMERATORS.

ONE TIMES ONE IS ONE.

AND WE PUT IT OVER

THE DENOMINATOR.

SO, WE MULTIPLY THOSE TWO

TOGETHER.

FOUR TIMES FOUR IS 16.

Vanessa writes the fraction 1/16.

She says, SO, MY ODDS OF ROLLING RED

TWICE IN A ROW

ON THIS WHEEL

ARE ONE OUT OF 16.

NOW, IF I'M PUTTING THAT ON

MY NUMBER LINE,

I KNOW THAT IT WOULD BE

ALMOST BETWEEN

IMPOSSIBLE AND UNLIKELY.

OKAY?

Vanessa points at the number line.

She says, SO, THIS IS A HARD GAME TO WIN,

TO GET TO ROLL--

OR TO SPIN RED TWICE IN A ROW.

BUT LET ME TRY, 'CAUSE I THINK

I WAS LUCKY ON THAT OTHER.

(LAUGHING)

THAT OTHER GAME.

I WAS PICKING A HEART. OKAY.

Vanessa spins the 4-colored lazy Susan wheel.

SO, UNFORTUNATELY, NO.

I ROLLED WHITE.

AND I ROLLED WHITE AGAIN.

SO, I WOULD NOT HAVE WON

ON MY GAME.

THE ODDS OF ME LOSING, THEN,

WOULD BE--

SO, THIS IS FOR A WIN.

AND THEN WE KNOW THAT

MY ODDS OF LOSING

WOULD BE 15 OUT OF 16.

SO, MUCH HIGHER

THAT I WOULD'VE LOST.

BECAUSE WE KNOW 15 OVER 16

PLUS ONE OVER 16

GIVES ME 16 OVER 16, OR A WHOLE.

OKAY? SO, UNFORTUNATELY,

I DIDN'T WIN THAT GAME.

Vanessa reveals a new sheet of paper on the display that reads, 3 heads in a row: 1/2 x 1/2 x 1/2

Vanessa continues, NOW, WHAT IF SOMEONE SAYS,

"CAN YOU FLIP A COIN

"SO THAT YOU GET HEADS

THREE TIMES IN A ROW?"

WELL, WHAT'S THAT PROBABILITY?

SO, ON THE FIRST ROLL,

I HAVE A ONE-IN-TWO SHOT,

BECAUSE WE TALKED ABOUT

HEADS OR TAILS

BEING THE TWO POSSIBILITIES,

AND WE SAID WE WANTED HEADS,

OKAY?

SO, THAT WOULD BE MY FIRST ROLL,

MY FIRST FLIP.

MY SECOND FLIP,

I HAVE THE SAME PROBABILITY.

AND MY THIRD FLIP, I HAVE TO GET

A ONE-OUT-OF-TWO SHOT

OF GETTING A HEAD.

WHAT IS THAT ALTOGETHER?

SO, WE CAN MULTIPLY

OUR FRACTIONS.

ONE TIMES ONE TIMES ONE,

YOU GET ONE.

OVER-- NOW, WE MULTIPLY

OUR DENOMINATORS TOGETHER.

TWO TIMES TWO IS FOUR.

TIMES TWO AGAIN IS EIGHT.

Vanessa writes the fraction 1/8.

She says, SO, I HAVE A ONE-OUT-OF-EIGHT

PROBABILITY

OF FLIPPING A COIN AND

RECEIVING HEADS, THREE IN A ROW.

THREE TIMES IN A ROW.

AGAIN, WE'RE LOOKING AT

THE "UNLIKELY" RANGE.

UM, SOMEWHERE IN BETWEEN HERE.

OKAY? SO, YOUR FRIEND

IS MORE LIKELY TO WIN

IF THEY SAID THAT

THEY COULD ROLL ANYTHING

BUT THREE HEADS IN A ROW.

IF THEY SAID THAT THEY COULD

ROLL EITHER A HEADS OR TAILS?

(LAUGHING)

AH, THAT WOULD BE SMART.

OKAY. SO, LET'S SEE IF I CAN

ROLL THREE HEADS IN A ROW.

Vanessa flips a coin and says,

ONCE, AND I PROMISE

I'M NOT CHEATING.

CAN YOU SEE THE REFLECTION?

OKAY.

She flips the coin again and says, NO. I GOT A TAIL.

OKAY? SO, I DIDN'T WIN AGAIN.

AND HOW DO WE KNOW THAT

IT WAS GOING TO BE DIFFICULT

FOR ME TO WIN THIS GAME?

BECAUSE WHEN WE PLOT IT

ON OUR NUMBER LINE,

WE SEE THAT ONE OUT OF EIGHT

IS A VERY SMALL FRACTION,

LESS THAN UNLIKELY.

SO, THAT GAME WOULD BE

VERY, VERY DIFFICULT TO WIN.

LET'S PLAY ONE MORE BEFORE

WE WATCH OUR NEXT EPISODE

OF

MATHXPLOSION.

Vanessa picks up a deck of cards and places a blue card with the fraction 26/52 on the display.

Vanessa says, UM, LET'S SEE IF I CAN

GET THESE ODDS HERE.

SO, WHAT DO YOU THINK

I'M GOING TO--

HOW CAN I WIN THIS GAME?

LET'S SAY I CAN PICK EITHER

TWO OF TWO DIFFERENT SUITS,

OR I COULD PICK, UM,

ONE RED CARD.

OKAY? SO, I KNOW THAT THERE ARE

26 RED CARDS IN THIS DECK.

AND THERE'S 26 BLACK CARDS

IN THIS DECK,

SO IT'S EQUALLY LIKELY THAT

I WOULD PICK A RED OR A BLACK.

SO, MY CHANCES ARE RIGHT IN

THE MIDDLE OF THAT NUMBER LINE,

THAT 0.5, OR ONE OVER TWO.

UM, LET'S GO THIS WAY.

ACTUALLY, NO. LET'S TRY IT.

LET'S DO IT THIS WAY AGAIN.

OKAY. SO, LET'S SEE MY ODDS OF

PICKING A BLACK CARD

ON THE TOP OF MY PILE.

Vanessa picks the 8 of hearts out of the deck.

Vanessa says, AND IT WAS A RED.

SO, UNFORTUNATELY, I DID NOT WIN

THE GAME

THAT I WOULD HAVE WON

IF I HAD DRAWN A BLACK CARD.

SO, I WAS EQUALLY LIKELY

TO WIN AND LOSE,

AND UNFORTUNATELY,

I TAKE THE LOSS ON THIS ONE.

SO, I WOULD LOVE FOR YOU TO

WATCH THIS NEXT EPISODE

OF

MATHXPLOSION.

IT'S GOING TO TEACH YOU

HOW SOCKS AND MATH TOGETHER

ARE AN AWESOME, AWESOME

MAGIC TRICK.

SO, CHECK IT OUT, AND I'LL

MEET YOU HERE AFTER THE VIDEO.

The animated sun rises.

(laser sounds)

Kids sing, WHAT A HIT

IT'S NOT A TRICK

IT'S

MATHXPLOSION

The MathXplosion logo appears.

The kids sing, JUST FOR YOU, COOL AND NEW

MATHXPLOSION

A brown-haired man with a neatly trimmed beard, carries a brown wooden drawer full of colorful socks.

He wears a red t-shirt with the MathXplosion logo on it.

The man says, DID YOU KNOW THAT I CAN FIND

TWO SOCKS OF THE SAME COLOUR

IN THIS MESSY SOCK DRAWER

WITH MY EYES CLOSED?

YEP, THAT'S RIGHT.

AND AS AMAZING

AS THAT SOUNDS ALREADY,

I NEED TO PICK

JUST FOUR SOCKS TO DO IT.

I'LL SHOW YOU HOW IT'S DONE.

YOU WON'T BELIEVE YOUR EYES.

The man opens the drawer. It is empty.

The man says, NEED SOME SOCKS, PLEASE.

GET SOME SOCKS.

The man stands behind a table.

I HAVE BEFORE ME

A DRAWER FULL OF SOCKS.

THESE SOCKS COME IN

THREE DIFFERENT COLOURS.

WE HAVE BLUE, GREEN AND PINK.

THE TOTAL NUMBER OF SOCKS

IN THE DRAWER

DOESN'T MATTER AT ALL,

AS LONG AS I KNOW

HOW MANY COLOURS THERE ARE.

IN THIS CASE, THREE COLOURS.

SO, WHAT I'M GOING TO DO IS

PULL JUST FOUR SOCKS

FROM THE DRAWER IN THE DARK.

AND I CAN GUARANTEE

THAT AT LEAST TWO

WILL BE OF THE SAME COLOUR.

LET'S TURN OFF THESE LIGHTS.

(CLAPPING)

GREAT. OH, BOY. THAT'S DARK.

(CAT YOWLING)

OH, SORRY, KITTY.

OKAY.

YOU KNOW, THIS IS WAY TOO DARK.

THIS ISN'T WORKING.

LET'S TURN THE LIGHTS BACK ON.

(CLAPPING)

LIGHTS?

(CLAPPING)

OH.

WELL, THAT DIDN'T WORK AT ALL.

(CHUCKLING)

I KNOW.

I'LL DO THIS BLINDFOLDED.

OKAY.

The man puts on a blindfold, then reaches into the drawer and pulls out socks.

He says, ONE, TWO, THREE.

ANY MATCHING COLOURS YET?

NO?

OKAY.

WELL, KEEP YOUR EYE ON

SOCK NUMBER...

...FOUR.

The man pulls out a second pink sock and says,

YES.

THE FIRST THREE SOCKS

WERE DIFFERENT COLOURS,

SO THE FOURTH ONE

HAS

TO MATCH.

IF YOU START WITH

THREE SOCK COLOURS,

PICKING FOUR SOCKS

GUARANTEES AT LEAST TWO SOCKS

OF THE SAME COLOUR.

AMAZING.

The man draws a yellow circle on a chalkboard, then taps the circle with his fist. The chalkboard becomes a monitor showing an animation of socks floating out of a dresser drawer.

The man says, THE LIKELIHOOD OF SOMETHING

HAPPENING,

LIKE CHOOSING

A SPECIFIC SOCK COLOUR,

IS CALLED PROBABILITY.

YOU CAN USE

THE SAME TRICK ON MITTENS, TOO.

TO GUARANTEE THAT YOU

FIND TWO MITTENS

OF THE SAME COLOUR IN THE DARK,

THE NUMBER OF MITTENS TO PICK UP

IS THE NUMBER OF MITTEN COLOURS

PLUS ONE.

THREE COLOURS, FOUR MITTENS.

Four mittens float above the dresser.

The man says, SO, THERE YOU HAVE IT.

I'VE SHARED YET ANOTHER

AMAZING SECRET:

HOW TO MATCH UP SOCKS

IN THE DARK.

TRY IT OUT YOURSELVES AT HOME.

BUT REMEMBER, USE CLEAN SOCKS.

(SNIFFING)

NOT SMELLY ONES.

PROBABILITY.

IT'S NOT MAGIC; IT'S MATH.

The drawer is full of socks. The Math Xplosion logo appears.

Text reads, produced by GAPC Entertainment. In association with TVO Kids. With the financial participation of Bell Fund, Canadian Media Fund and Shaw Rocket Fund.

The animated sun rises.

Vanessa says, WELCOME BACK.

LET'S PUT IT ALL TOGETHER NOW.

REVIEWING OUR DEFINITION

OF PROBABILITY,

THE LIKELIHOOD

OF SOMETHING HAPPENING.

WE'VE SHOWN IT THROUGH

A FRACTION AND NUMBER LINE.

AND WE USE PROBABILITY TO

MAKE DECISIONS AND PREDICTIONS,

ESPECIALLY THE WEATHER.

SO, THIS IS THE TIME FOR YOU

TO GET INVOLVED.

IF YOU HAVE THOSE MARKERS

AND THAT PAPER

AND DIFFERENT FORMS OF

PROBABILITY GAMES,

I WOULD LOVE FOR YOU

TO GET THAT READY

AND BRING IT TO YOUR WORK AREA.

AND WE ARE GOING TO

PLAY A LITTLE GAME.

SO, YOU, ON A PIECE OF PAPER,

WILL WRITE PROBABILITY EVENTS

THAT COULD HAPPEN IN WORDS.

OKAY?

SO, FOR EXAMPLE...

Vanessa places a green card on the tabletop display. It reads, “I win the lottery”.

Vanessa continues, ...MY FIRST POSSIBLE EVENT

THAT COULD HAPPEN?

I WIN THE LOTTERY.

OKAY? SO, I'M PICKING AN EVENT

THAT COULD HAPPEN.

AND THEN,

WHAT I'M GOING TO DO IS

THINK ABOUT THE LIKELIHOOD

OF IT OCCURRING. OKAY?

SO, YOU COULD THEN EXCHANGE

YOUR EVENT WITH A FRIEND,

MAYBE WITH A PARENT.

MAYBE TALK TO, UM,

ANOTHER ADULT IN YOUR LIFE,

LIKE A TEACHER.

ASK THEM WHAT ARE THE ODDS THAT

THEY'RE GOING TO WIN THE LOTTERY

THIS WEEK, AND THEN

PLOT IT ON YOUR NUMBER LINE.

Vanessa holds up the number line.

She continues, SO, IF I SAID TO MY TEACHER,

"MISTER OR MISS,

WHAT ARE THE ODDS

THAT YOU'RE GOING TO WIN

THE LOTTERY THIS WEEK?"

YOU CAN TELL THEM THAT,

IF THEY'RE UNSURE,

THAT IT WOULD BE SOMEWHERE

IN THIS RANGE

THAT THEY WIN THE LOTTERY.

OKAY? SO, THIS EVENT,

WE KNOW THAT OCCURS--

ONE OUT OF 33,000,000

ARE THE ODDS

OF WINNING THE LOTTERY.

SO, VERY, VERY UNLIKELY

THAT YOU WIN THE LOTTERY.

YOU COULD COME UP WITH

ANOTHER EVENT

THAT YOU COULD ASK YOUR FRIEND

MIGHT HAPPEN.

YOU FLIP A COIN

AND YOU LAND ON TAILS.

NOW, KNOWING WHAT YOU DO

ABOUT PROBABILITY,

YOU KNOW THAT YOU HAVE

AN EQUALLY LIKELY PROBABILITY,

ONE OVER TWO, BECAUSE TAILS--

THERE'S EITHER HEADS OR TAILS

AS THE POSSIBLE OUTCOMES,

AND YOU LAND ON TAILS.

SO, YOU'RE EQUALLY LIKELY, 50%.

AND THEN, WITH YOUR FRIEND

OR YOUR GUARDIAN OR PARENT,

THEY COULD PLOT THIS

ON THE NUMBER LINE.

I FLIP A COIN AND LAND ON TAILS.

NOW, YOU MIGHT WANT TO GET

SOME CERTAIN ONES IN THERE, TOO.

WE ALL ARE HOPING FOR THIS:

SUMMER WILL COME.

SO, YOU MAKE THAT EVENT

ON A PIECE OF PAPER.

YOU WRITE IT DOWN,

AND YOU ASK YOUR FRIEND,

"WHERE CAN IT BE PLACED

ON THE NUMBER LINE?"

IS THAT IMPOSSIBLE,

EQUALLY LIKELY, OR CERTAIN?

AND WE KNOW CERTAINLY,

EVERY SEASON

COMES WITHIN THE YEAR.

SO, IT'S CERTAIN THAT

THE SUMMER WILL COME,

AND THAT SUMMER BREAK

IS INEVITABLE.

OKAY? SO, WHAT WE'RE PRACTISING

WHEN WE DO THIS GAME,

WE'RE TALKING ABOUT

THE PROBABILITY

OF LIFE EVENTS HAPPENING.

AND ON OUR NUMBER LINE,

WE'RE PLOTTING THEM ON A SCALE

BETWEEN ZERO, HALF, AND ONE

AS OUR BENCHMARK NUMBERS.

OKAY? SO, THIS IS GETTING US

IN THE FRAME OF MIND

OF USING THESE TERMS

THAT WE'RE TALKING ABOUT,

PROBABILITY OF EVENTS.

Vanessa puts a green card on the display that reads, viewers are in grades 4, 5, and 6!

Vanessa says, OUR VIEWERS HERE

ARE IN GRADES 4, 5 AND 6.

THAT IS ALMOST CERTAIN.

OUR KEY DEMOGRAPHIC

FOR THIS VIDEO,

THE CURRICULUM,

IS IN THE JUNIOR GRADES.

SO, ALMOST CERTAINLY,

MANY OF OUR VIEWERS ARE--

MOST OF OUR VIEWERS

ARE, UM, IN THOSE GRADES.

BETWEEN LIKELY AND CERTAIN.

AND FINALLY, FOR A LAUGH,

"I LEARN HOW TO SKATEBOARD."

SO, KNOWING ME, I--

VERY HARD FOR ME TO LEARN THAT

AT MY AGE.

SO, THIS WOULD BE SOMETHING

THAT'S UNLIKELY

THAT I WOULD LEARN HOW TO DO.

SO, IF YOU KNEW SOMETHING ABOUT

YOUR FRIEND,

MAYBE THEY WOULD SAY,

"YOUR FAVOURITE FOOD IS CHIPS,"

FOR EXAMPLE.

AND YOU WOULD SAY,

"YOU KNOW WHAT? IT CERTAINLY IS.

YOU GOT THOSE ODDS RIGHT ON."

SO, YOU CAN WRITE

DIFFERENT LIFE EVENTS

AND SHARE THEM WITH A PARTNER

OR YOUR PARENTS

AND SEE WHERE THEY FALL

ON THE NUMBER LINE.

FOR YOUR SECOND GAME,

Vanessa puts a sheet of paper on the tabletop display.

She says, I WOULD LOVE FOR YOU TO USE

EITHER PLAYING CARDS,

SPINNERS, OR A DIE,

AND HONESTLY,

ALL CAN BE HOMEMADE

WITHIN A FEW MINUTES.

AND YOU'RE GOING TO STATE

A PROBABILITY TO WIN.

SO, IF I SAID I WANT TO MAKE

A GAME

THAT HAS A ONE-IN-FOUR

PROBABILITY TO WIN,

I WOULD MAKE A SPINNER

WITH FOUR SECTIONS ON IT.

IF I SAID I WANTED TO MAKE

A SPINNER--

OR SORRY, A GAME WITH A SPINNER

THAT HAS A PROBABILITY OF ONE

OUT OF SIX AFTER EVERY SPIN,

WE COULD MAKE A SPINNER

LIKE THIS ONE HERE

THAT HAS SIX SECTIONS.

OKAY? SO, IT'S UP TO YOU.

YOU CAN CHOOSE EITHER A SPINNER,

PLAYING CARDS, A DICE, COINS.

WHAT KIND OF GAME

WOULD YOU LIKE TO CREATE?

SO, FOR MY DICE GAME

THAT WE'RE GOING TO PLAY

A LITTLE BIT LATER,

IT'S CALLED MULTIPLY TO WIN.

I'M GOING TO ROLL MY TWO DICE,

AND THE ONLY WAY I CAN WIN

IS IF I ROLL TWO--

THE PRODUCT OF THE TWO ROLLS

HAS TO BE 36.

WHAT DOES THAT MEAN?

HOW CAN I GET 36

WHEN I MULTIPLY

MY TWO ROLLS TOGETHER?

IT MEANS THAT I'D HAVE TO HAVE

MY FIRST DICE, ROLL A SIX,

AND MY SECOND DICE,

ALSO ROLL A SIX.

Two brown dice sit on the table in front of Vanessa.

She says, BECAUSE SIX TIMES SIX

GIVES ME A PRODUCT OF 36.

WHAT ARE THE ODDS OF GETTING 36

AS MY PRODUCT?

WELL, I KNOW I HAVE

A ONE-OUT-OF-SIX CHANCE

OF ROLLING A SIX ON A DICE,

ON A SIX-SIDED DICE.

I ALSO AGAIN HAVE

A ONE-OUT-OF-SIX PROBABILITY

OF ROLLING A SIX

ON MY SECOND ROLL,

BECAUSE IT'S A SIX-SIDED DICE

DOWN HERE

AND THE NUMBER SIX

ONLY OCCURS ONE TIME.

WHEN I MULTIPLY

THOSE TWO NUMBERS TOGETHER,

ONE TIMES ONE IS ONE.

I MULTIPLY MY DENOMINATORS

TOGETHER.

SIX TIMES SIX IS 36.

SO, MY PROBABILITY

OF WINNING MY GAME

IS ONE OUT OF 36.

NOW, IF AGAIN, WE'RE USING IT

ON A NUMBER LINE,

I CAN SEE THAT

IT'S QUITE UNLIKELY

THAT I WILL WIN THIS GAME,

BUT WHY NOT HAVE FUN AND TRY?

SO, GO AHEAD

AND MAKE YOUR OWN GAME,

WHATEVER YOU CHOOSE,

WHATEVER YOU'D LIKE YOUR

PROBABILITY TO BE.

AND PLAY IT WITH A FRIEND,

A SIBLING, A PARENT, A GUARDIAN,

AND LET ME KNOW

HOW MUCH FUN YOU'RE HAVING.

The animated sun rises.

Vanessa continues, HOW ARE THE GAMES GOING?

ARE YOU HAVING A LOT OF FUN?

LET'S TRY MINE.

SO, WE HAD TALKED ABOUT

THEORETICAL PROBABILITY

BEING THE NUMBER OF FAVOURABLE

OUTCOMES

OVER THE NUMBER

OF POSSIBLE OUTCOMES.

AND WE KNOW IN MY GAME,

I REQUIRE BOTH NUMBERS

TO BE SIX,

SO THAT THEY MULTIPLY TO

A PRODUCT OF 36.

SO, I HAVE A ONE-IN-36

PROBABILITY

OF ME WINNING MY GAME.

SO, IT'S NOT VERY LIKELY,

BUT WHY NOT HAVE

A LOT OF FUN DOING IT?

SO, I'M GOING TO ROLL

MY FIRST DICE.

LET'S SEE WHAT I GET

AS MY FIRST.

Vanessa rolls a die and says, I GET A FIVE.

SO, UNFORTUNATELY,

I KNOW THAT NO MULTIPLICATION,

NO PRODUCT WITH A FIVE,

WILL EQUAL 36.

SO, I DIDN'T WIN

THAT FIRST TIME.

LET'S TRY IT AGAIN.

Vanessa rolls the die and says,

I GOT A FOUR.

SO AGAIN, UNFORTUNATELY,

I DIDN'T WIN.

BUT THE PROBABILITY TOLD ME

THAT IT'S VERY UNLIKELY

THAT I WOULD WIN.

OKAY? SO, I CAN MAKE A DECISION

BASED ON HOW LIKELY THE OUTCOME

IS TO HAPPEN GOING FORWARD.

SO, MAYBE AGAIN,

IF I WANTED TO REALLY BEAT

MY FRIENDS,

I COULD SAY, "YOU KNOW WHAT?

IF YOU ROLL TWO SIXES,

YOU CAN WIN," 'CAUSE I KNOW THAT

IT'S VERY, VERY DIFFICULT

FOR THEM TO WIN,

TO ROLL TWO SIXES.

SO, YOU CAN HAVE A LOT OF FUN

WITH YOUR FRIENDS THAT WAY, TOO.

AGAIN, WE'RE GOING TO USE

PROBABILITY IN OUR LIVES

TO MAKE DECISIONS

AND PREDICTIONS.

IF WE KNOW THAT THERE'S

A 10% CHANCE OF RAIN,

WE KNOW THAT IT'S VERY UNLIKELY

THAT YOU HAVE TO BRING

THAT UMBRELLA TO SCHOOL

THAT DAY.

COMPARED TO A 90% CHANCE

OF RAIN,

WHERE IT'S ALMOST CERTAIN

TO RAIN,

YOU'RE GOING TO NEED TO MAKE

A CHANGE OF PLAN

AND PACK THAT UMBRELLA

INTO THAT BACKPACK

BEFORE YOU GET IT--

AS YOU GO OFF TO SCHOOL.

Vanessa holds up the number line.

She says, USING THAT NUMBER LINE,

PLOTTING FROM IMPOSSIBLE

OR NEVER

ALL THE WAY TO CERTAIN, OKAY,

THIS IS GOING TO HELP YOU

UNDERSTAND

HOW LIKELY AN EVENT WILL OCCUR.

IN TERMS OF GAMES,

IN TERMS OF YOUR FAVOURITE TEAM

WINNING THE STANLEY CUP,

THEY'RE ALL EQUALLY AS LIKELY

TO WIN

AT THE BEGINNING OF THE SEASON.

The caption appears that reads, Junior 4-6. Teacher Vanessa.

Vanessa says, I HOPE YOU HAD A LOT OF FUN

WITH TODAY'S EPISODE.

I KNOW I DID. KEEP PRACTISING

THOSE POSITIVE AFFIRMATIONS.

KEEP PRACTISING

USING PHYSICAL ACTIVITY

AS A WARMUP TO GET YOU READY

FOR LEARNING AND EXPLORING,

AND I'LL CATCH YOU NEXT TIME

ON ANOTHER EPISODE

OF

TVOKIDS POWER HOUR

OF LEARNING.

(soft upbeat music plays)

Text reads, TVO kids would like to thank all the teachers involved in the Power Hour of learning as they continue to teach children of Ontario from their homes.

TVO Kids Power Hour of Learning. TVO. Copyright, The Ontario Educational Communications Authority 2021

A title screen over a blue sky reads, Today’s Junior Lesson: Predicting Through Probability.

A female announcer says,

WELCOME TO

TVOKIDS POWER HOUR

OF LEARNING.

A brown haired woman wearing glasses and a leopard print shirt, sits at a table in her home.

A black and white photograph of downtown Toronto hangs on the wall behind her.

The woman says, HELLO, STUDENTS. HOW ARE YOU?

WELCOME TO ANOTHER EPISODE OF

TVOKIDS POWER HOUR OF LEARNING.

A caption appears that reads, Junior 4-6. Teacher Vanessa.

The woman continues, MY NAME IS TEACHER VANESSA,

AND I'M SO EXCITED TO SPEND

THE NEXT 60 MINUTES TOGETHER

LEARNING, HAVING A LOT OF FUN,

AND SHARING A FEW LAUGHS

TOGETHER.

BUT BEFORE WE BEGIN,

I'M HOPING THAT

YOU'VE BEEN PRACTISING

OUR POSITIVE AFFIRMATIONS THAT

WE LEARNED A FEW WEEKS AGO.

THESE ARE POSITIVE STATEMENTS

CALLED MANTRAS,

AND THEY HELP US BUILD

OUR SELF-CONFIDENCE

BY REPEATING THEM

OVER AND OVER EACH DAY.

SO, I'M GOING TO TELL YOU

OUR THREE MANTRAS,

AND I WOULD LOVE FOR YOU

TO REPEAT AFTER ME.

ARE YOU READY?

I AM CAPABLE.

LET ME HEAR YOU.

Vanessa holds her hand to her ear.

I AM A MATH PERSON.

GOOD JOB. AND I CAN DO IT.

AWESOME. I CAN HEAR YOU

ALL THE WAY FROM STONEY CREEK.

SO, TODAY WE'RE GOING TO BE

TALKING ABOUT PROBABILITY.

WHAT ARE THE ODDS

OF SOMETHING HAPPENING?

AND BEFORE WE BEGIN,

I WAS THINKING THAT

I COULD BRING MY SON CHASE OUT

TO PLAY A PROBABILITY GAME

AND GET US WARMED UP

FOR SOME GREAT LEARNING

OVER THE NEXT HOUR.

A young brown-haired boy, Chase, hops behind Vanessa. He wears a black T-shirt

Vanessa says, WELCOME, CHASE.

COME ON IN.

SO, WHAT WE'RE GOING TO

BE DOING--

JUST STAND BESIDE ME,

RIGHT HERE.

RIGHT HERE,

ON THE TABLE.

ARE YOU READY TO PLAY

A MATH GAME?

A caption reads, Junior 4-6. Chase.

Chase says, YEAH!

Vanessa says, OKAY. SO, STAND UP

NICE AND STRAIGHT

SO EVERYBODY

CAN SEE YOU.

OKAY. SO, I AM GOING TO

ROLL A DICE,

AND WHATEVER NUMBER

WE LAND ON,

THAT'S HOW MANY

EXERCISES--

YEAH. ARE YOU READY

TO SHOW THE KIDS

SOME EXERCISES?

SO, BEFORE YOU BEGIN,

MAKE SURE THAT YOU HAVE

A BIG SPACE

TO DO SOME EXERCISES,

JUST LIKE CHASE IS.

MAKE SURE

YOU CAN SPREAD OUT

AND HAVE A LOT

OF ROOM.

SO, WE'RE GOING TO

GET OUR BODIES READY

SO THAT OUR MINDS

WILL BE READY TO LEARN.

I'M GOING TO ROLL

THE FIRST DICE,

AND IT LANDS ON

A FOUR.

Vanessa holds up a large die made of brown cardboard paper.

Vanessa says, SO, CHASE, DO YOU MIND

DOING FOUR JUMPING JACKS?

Chase does jumping jacks and counts, OKAY. ONE, TWO, THREE, FOUR.

Vanessa says, AWESOME. NEXT ROLL.

Vanessa rolls the die and says, A ONE. HOW ABOUT YOU DO

ONE NECK CIRCLE?

Chase and Vanessa do a neck circle.

Vanessa says, NEXT ROLL, WE HAVE

A ONE AGAIN.

HOW ABOUT ONE HIGH KNEE?

Chase raises his left knee.

Vanessa says, OKAY. LAST ROLL.

ARE YOU READY?

Chase says, YEAH.

Vanessa rolls the die and says, SIX. LET'S DO

SIX ARM CIRCLES

TO GET OUR ARMS READY TO

WRITE AND PLAY SOME GAMES.

Chase circles his arms and counts, ONE, TWO, THREE, FOUR,

FIVE, SIX.

Vanessa says, ALL RIGHT. AND LET'S TAKE

SOME BIG, DEEP BREATHS

BEFORE WE BEGIN,

CHASE.

(BOTH INHALING AND EXHALING)

Vanessa says, ONE MORE.

(INHALING AND EXHALING)

Vanessa continues, BREATHE OUT. AND SAY, "BYE

AND THANK YOU" TO EVERYBODY.

Chase waves and says, BYE.

Vanessa says, THANK YOU

FOR JOINING US, CHASE.

An animated sun rises.

Notes on a tabletop display beside Vanessa read, Probability, the likelihood of something happening.

Shown through a fraction and number line. Use probability to make decisions and predictions.

Vanessa says, SO, TODAY, WE'RE GOING TO

TALK ABOUT PROBABILITY,

THE LIKELIHOOD

OF AN EVENT OCCURRING.

HAVE YOU EVER WONDERED

WHAT THE WEATHER PERSON

IS TALKING ABOUT WHEN THEY SAY,

"THERE'S A 50% CHANCE

OF RAIN OR SNOW"?

OR IF YOU HAVE A VERY SMALL

CHANCE OF WINNING THE LOTTERY?

WHAT ARE THEY TALKING ABOUT?

TODAY, I'M GOING TO SHOW YOU

HOW YOU CAN SOLVE

FOR PROBABILITY

USING FRACTIONS

AND A NUMBER LINE.

WE'RE GOING TO USE PROBABILITY

TO MAKE DECISIONS

AND FUTURE PREDICTIONS.

SO, IF YOU HEARD THAT

THERE WAS A SNOWSTORM COMING,

YOU WOULD PRETTY--

YOU'D BE PRETTY WELL

TO BRING SNOW PANTS

AND MITTENS TO SCHOOL THAT DAY,

SO YOU'RE PREPARED FOR

THE WEATHER.

WE'RE GOING TO PLAY SOME

FUN GAMES TODAY WITH SPINNERS,

DICE AND CARDS.

SO, I WOULD LOVE FOR YOU

TO GET THOSE MATERIALS

IF YOU HAVE THEM LAYING AROUND,

OR YOU COULD MAKE

YOUR OWN CARDS.

YOU COULD MAKE YOUR OWN DICE.

I MADE THESE OUT OF

A PIECE OF CARDBOARD.

IT'S VERY SIMPLE. ALL YOU NEED

TO MAKE THE CARDBOARD DIE

ARE TAPE, CARDBOARD AND MARKERS.

IF YOU HAVE SOMETHING LIKE

A LAZY SUSAN LAYING AROUND--

YOUR PARENTS

WILL KNOW WHAT THAT IS--

YOU CAN TAPE SOME PAPER TO IT

AND IT'LL SPIN LIKE A SPINNER,

OKAY?

Vanessa holds up a lazy susan covered with colored paper in white, blue, red and yellow quadrants.

Vanessa says, I USED JUST YOUR RUN-OF-THE-MILL

DECK OF CARDS.

IF YOU HAVE A COIN OR TWO,

WE COULD DO SOME COIN TOSSES

LATER ON.

I'M GOING TO SHOW YOU SOME

REALLY COOL GAMES AND ACTIVITIES

YOU COULD DO WITH YOUR FRIENDS.

BUT BEFORE WE DO, LET'S WATCH

THIS EPISODE OF

LADY VOCAB,

WHO'S GOING TO GO INTO

THE DEFINITION OF PROBABILITY

USING A REALLY COOL SONG.

CHECK IT OUT, AND I'LL CATCH YOU

BACK HERE AFTER.

The animated sun rises.

A title screen reads, The Lady Vocab Show.

Professor P stands in a dark room in front of a monitor ‘with Lady Vocab’ written several times on it.

He wears a black sweater with a large letter P on the front. He has short dark hair and wears glasses.

Professor P says, HEY THERE, WORD FANS,

AND WELCOME TO

THE

LADY VOCAB SHOW.

I'M YOUR HOST,

PROFESSOR P.

AND NOW TO INTRODUCE

THE LONG-WINDED LADY HERSELF,

LADY VOCAB.

Lady Vocab stands behind a microphone.

She has shoulder length blonde hair and wears large sparkling silver glasses, and a black and white costume with the words window, shuttle, machine, and package written on it.

She says, THANKS, PROFESSOR.

ARE YOU READY

TO ROCK THE WORD?

Professor P says, YES, INDEEDY, MILADY.

THE WORD IS "PROBABILITY,"

WHICH IS A TERM THAT MEANS

HOW LIKELY SOMETHING

IS TO HAPPEN.

Lady Vocab says, HIT IT.

(Electronic music plays)

She sings, P-R-O-B-A-B-I-L-I-T-Y

Professor P says, PROBABILITY.

Lady Vocab sings, THE CHANCES THAT

YOU'RE LIKELY TO SUCCEED

JUST USE PROBABILITY

Professor P says, MM-HMM.

Lady Vocab sings, TOSS A COIN, IT'S 50-50

Professor P says, COULD BE HEADS

OR TAILS.

Lady Vocab sings, THE OUTCOME

IS FOR YOU TO SEE

Professor P says, THAT'S RIGHT.

Lady Vocab sings, PROBABILITY

SEEMS LIKELY

Professor P says, MM-HMM.

COULD BE.

Lady Vocab sings, PROBABILITY

CHANCES MAKE YOU LUCKY

Professor P says, HOW LIKELY?

Lady Vocab sings, PROBABILITY.

Professor P says, HMM. WELL, THERE YOU HAVE IT.

THE LIKELIHOOD THAT

I'LL SEE YOU NEXT TIME?

100%, WORD FANS. BYE FOR NOW.

Lady Vocab sings, PROBABILITY

YOU'RE SO LUCKY, PROBABILITY

A red logo over a black background reads, TVO kids. Copyright, The Ontario Educational Commissions Authority MMXIV

The animated sun rises.

Vanessa says, WELCOME BACK.

SO, TODAY WE'RE GOING TO TALK

ABOUT THEORETICAL PROBABILITY.

The caption reads, Junior 4-6. Teacher Vanessa.

A formula written on the tabletop display reads, theoretical probability equals number of favorable outcomes divided by number of possible outcomes.

Vanessa continues, WHAT DOES THAT MEAN?

WHAT ARE YOUR ODDS OF WINNING

WHEN YOU PLAY A GAME?

WHAT ARE YOUR ODDS

OF ROLLING ANY NUMBER ON A DICE?

Vanessa holds up a die.

She continues, WHAT ARE THE ODDS OF GETTING

A HEADS OR TAILS

WHEN YOU FLIP A COIN?

Vanessa holds up a coin.

She continues, AND IF YOU WANTED TO PLAY A GAME

WITH YOUR FRIENDS,

WHAT ARE THE ODDS OF PICKING UP

AN EIGHT IN CRAZY EIGHTS?

LET'S FIGURE THIS OUT.

SO, THEORETICAL PROBABILITY,

OR PROBABILITY,

IS KNOWN AS THE NUMBER

OF FAVOURABLE OUTCOMES

OVER, OR DIVIDED BY

IN A FRACTION FORM,

THE NUMBER OF POSSIBLE OUTCOMES.

SO, WHAT DOES THAT MEAN?

LET'S SAY I HAVE A DICE.

WE KNOW THAT THERE ARE SIX SIDES

TO A DICE,

AND EVERY SIDE HAS A NUMBER

RANGING FROM ONE TO SIX.

Vanessa rolls the die and says, SO, IF I WERE TO ROLL THIS DICE

AND I GET THE NUMBER SIX,

TECHNICALLY I HAVE

A ONE-OUT-OF-SIX PROBABILITY

OF GETTING ANY NUMBER

ON THIS DICE.

IN THIS CASE, I DID ROLL A SIX.

OKAY?

SO, LET'S SAY

I SAID TO MY FRIEND,

"IF I ROLL A FIVE,

I WIN THE GAME."

WHAT ARE MY ODDS OF WINNING?

I KNOW THAT I HAVE TO ROLL

JUST A FIVE,

SO THAT WOULD JUST BE A ONE,

LIKE WE HAVE HERE.

Vanessa holds up a blue card with the fraction 1/6 written on it.

She says, AND THERE ARE

SIX POSSIBLE OUTCOMES

'CAUSE THERE ARE SIX NUMBERS

ON A DICE.

SO, I HAVE A ONE-IN-SIX ODD

OF WINNING THE GAME.

LET'S SEE IF I DID WIN.

Vanessa rolls the die.

She says, NO. I ROLLED A FOUR.

SO UNFORTUNATELY,

MY FRIEND WON THAT ROUND.

FORTUNATELY FOR HER.

OKAY?

Vanessa removes the formula from the display, then picks up the lazy Susan spinner.

She says, LET'S TRY PLAYING WITH

OUR SPINNER.

AND WE HAVE

ONE, TWO, THREE, FOUR

DIFFERENT-COLOURED SECTIONS.

THAT MEANS THE SPINNER

CAN LAND ON

ANY ONE OF THE FOUR SECTIONS.

SO, MY POSSIBILITY--

PROBABILITY OF LANDING

ON THE WHITE, FOR EXAMPLE,

IS ONE OVER FOUR.

MY PROBABILITY OF LANDING

ON THE BLUE

IS ONE OUT OF THE TOTAL OF FOUR

DIFFERENT OPTIONS THERE ARE.

SO, YOU MIGHT SAY

TO YOUR FRIEND,

"IF I LAND ON RED, I WIN,

"BUT IF YOU LAND--

WHEN YOU SPIN AND YOU LAND

ON BLUE, YOU WIN."

SO, LET'S JUST SAY-- LET'S TRY.

I'M GOING TO SAY IF I LAND

ON RED, I GET ONE POINT.

Vanessa spins the spinner and says,

SO, I HAVE MY SPINNER.

I'M GOING TO TURN IT AROUND

AND UNFORTUNATELY,

I LANDED ON--

OH, WAIT, (UNCLEAR).

OH, NO. I LANDED ON THE WHITE.

SO, I DIDN'T GET A POINT, OKAY?

SO, LET'S SAY

IT'S MY FRIEND'S TURN.

AND THIS IS HARDER THAN IT SEEMS

TO HOLD.

(LAUGHING)

Vanessa spins the spinner and says,

AND IT LANDS ON BLUE,

BUT SHE NEEDED RED TO WIN.

SHE DOESN'T WIN.

SO, EITHER WAY, ONE OF US--

OR EACH OF US, I SHOULD SAY,

HAS A ONE-IN-FOUR CHANCE

OF WINNING THAT GAME.

IF I SAID I NEED TO LAND

ON RED

OR

BLUE TO WIN,

WHAT IS MY POSSIBILITY NOW,

MY PROBABILITY OF WINNING?

WE HAVE ONE-HALF.

WHY IS THAT ONE-HALF?

BECAUSE I COULD WIN ONE, TWO

OF A POSSIBLE

ONE, TWO, THREE, FOUR.

SO, TWO OUT OF FOUR

IS THE SAME AS

HAVING THE ODDS

OF HAVING ONE-HALF.

Vanessa holds up a blue card with the fraction 1/2 on it.

She says, SO, PLOTTING THIS

ON A NUMBER LINE,

I'M GOING TO SHOW YOU

SOME TERMS...

Vanessa picks up a long brown sheet of paper with a number line drawn on it.

Notes on the line from left to right read, impossible, unlikely, equally likely, likely, and certain.

The number 0 is at the left end. The number 1 is at the right.

Vanessa continues, ...THAT YOU ARE GOING TO BE

USING

IN MATHEMATICS FOR PROBABILITY.

I LOVE THE NUMBER LINE.

SO, IN THIS CASE

FOR PROBABILITY,

WE HAVE "UNLIKELY"

AND "IMPOSSIBLE"

STARTING AT THE ZERO.

SO, FOR EXAMPLE, YOUR ODDS

OF WINNING THE LOTTERY

ARE VERY, VERY UNLIKELY.

NOT IMPOSSIBLE,

'CAUSE "IMPOSSIBLE" MEANS

IT COULD NEVER HAPPEN.

BUT SOMEWHERE IN THE REALM OF

UNLIKELY TO IMPOSSIBLE.

SO, "IMPOSSIBLE" COULD BE

"THE SUN WON'T RISE TOMORROW,"

WHEN WE KNOW THAT CERTAINLY,

THE SUN WILL RISE EVERY DAY.

SO, WE'RE GOING TO MOVE

FROM IMPOSSIBLE TO UNLIKELY.

LIKE WE SAID,

WINNING THE LOTTERY,

LIKE WE SAID, SPINNING, UM,

MAYBE A WHEEL THAT HAD

A HUNDRED NUMBERS ON IT

AND YOU HAVE TO GET

ONE OF THE NUMBERS.

IT'S VERY UNLIKELY THAT

THE WHEEL WILL SPIN

ON YOUR NUMBER,

FROM ONE OUT OF A HUNDRED.

OKAY? AGAIN, NOT IMPOSSIBLE,

'CAUSE IT MIGHT HAPPEN.

BUT IT COULD BE UNLIKELY.

"EQUALLY LIKELY" MEANS

SOMETHING WILL HAPPEN

AS LIKELY AS IT WILL NOT HAPPEN.

SO, IF I PICK UP A COIN,

FOR EXAMPLE,

I KNOW THAT IT HAS A HEAD

AND A TAIL.

AND BECAUSE THERE'S

ONLY TWO OPTIONS, AGAIN,

I HAVE A ONE-OUT-OF-TWO ODD

OR PROBABILITY

THAT I WOULD ROLL-- OR, SORRY.

FLIP A COIN

AND LAND ON A HEAD.

I HAVE A ONE-IN-TWO PROBABILITY,

THEN,

THAT IT WOULD ALSO--

IT WOULD LAND ON A TAIL.

OKAY? SO, WHEN SOMETHING

IS EQUALLY LIKELY TO HAPPEN

AS IT'S

NOT LIKELY TO HAPPEN,

YOU HAVE A 50-50 CHANCE,

A ONE-OUT-OF-TWO SHOT,

IT IS EQUALLY LIKELY.

A yellow star is in the middle of the number line over the number 0.5.

Vanessa says, UM, SO, FOR SOMETHING TO BE

LIKELY TO HAPPEN,

WE CAN TALK ABOUT SOMETHING LIKE

IF THE WEATHER PERSON SAYS

THERE'S A 75% CHANCE

OF RAIN TODAY,

THAT IS LIKELY

THAT IT WILL HAPPEN.

HOW DO WE KNOW? WE KNEW THAT

SOMETHING CLOSER TO ONE

IS ABSOLUTELY CERTAIN TO HAPPEN.

SO, FOR EXAMPLE,

IF WE SAID YOU HAVE, UM--

IF YOU SPUN A WHEEL

AND IF YOU GOT ANY OF

THE THREE COLOURS EXCEPT WHITE,

YOU WIN, THAT IS LIKELY

THAT YOU WILL WIN THAT GAME,

BECAUSE YOU COULD LAND

ON YELLOW, RED, BLUE,

AND STILL WIN.

THE ONLY WAY YOU WOULD LOSE IS

IF YOU LANDED ON WHITE.

SO, THAT IS

A LIKELY PROBABILITY

THAT YOU WILL WIN.

SOMETHING CERTAIN IS THAT

YOU WILL TURN PLUS-ONE

ON YOUR NEXT BIRTHDAY.

SO, IF YOU ARE NINE, ON YOUR

NEXT BIRTHDAY YOU WILL TURN 10.

IF YOU'RE 10,

ON YOUR NEXT BIRTHDAY

YOU WILL CERTAINLY TURN 11.

YOU ARE AN AWESOME PERSON.

THAT IS CERTAIN.

SO, THAT'S 100% POSSIBILITY.

YOU'RE GREAT AT MATH?

100% POSSIBILITY. TRUST ME.

OKAY? SO, WE HAVE THE RANGE OF

SOMETHING IMPOSSIBLE HAPPENING,

OKAY?

SO AGAIN, WE SAID THAT

UNFORTUNATELY,

IF YOU THOUGHT THAT

THE SUN WILL NOT RISE TOMORROW,

IMPOSSIBLE.

YOU MIGHT WIN THE LOTTERY?

SOMEWHERE IN THE REALM

OF UNLIKELY AND IMPOSSIBLE.

SO, EVERY DAY, WHEN YOU BUY

YOUR LOTTERY TICKET,

AND YOU HAVE A 1 IN 33,000,000

CHANCE OF WINNING,

UNFORTUNATELY THE ODDS ARE

VERY, VERY LOW THAT YOU WIN,

BUT THEY'RE NOT IMPOSSIBLE.

SO, WE HAVE

"WINNING THE LOTTERY"

WOULD BE SOMEWHERE POSSIBLY

CLOSER TO THE ZERO HERE.

BUT DON'T GIVE UP HOPE, FRIENDS,

AS YOU GET OLDER.

(LAUGHING)

AGAIN, "EQUALLY LIKELY,"

WE'RE TALKING ABOUT

FLIPPING A COIN

AND THERE'S ONLY TWO OPTIONS.

(CLEARING THROAT)

WE'RE

TALKING ABOUT PLAYING CARDS,

WHEN YOU ONLY HAVE

RED OR BLACK SUITS.

Vanessa holds up two playing cards.

She continues, YOU'RE EQUALLY LIKELY

TO PICK UP A RED CARD

AS YOU ARE A BLACK CARD.

WE HAVE SOMETHING "LIKELY"

AS 75%,

OR THREE OVER FOUR.

WE TALKED ABOUT THE SPINNER.

WE SAID YOU WON--

WHEN THE GAME IS YOU CHOOSE

RED, YELLOW OR BLUE

OUT OF A TOTAL OF FOUR OPTIONS,

IT'S LIKELY THAT YOU WILL WIN.

AND THEN "CERTAIN," WE TALKED

ABOUT YOU GETTING A YEAR OLDER

FOR YOUR AGE NEXT YEAR, AND FOR

THE SUN SETTING THE NEXT DAY.

SO, WHEN YOU'RE WATCHING TV

AND MAYBE YOU'RE CATCHING

YOUR PARENTS WATCHING THE NEWS,

AND THE WEATHER PERSON SAYS,

"THERE'S A 10% CHANCE

OF PRECIPITATION TONIGHT,"

Vanessa holds a sheet of paper that reads, unlikely, 10%, 1/10, 0.1.

She continues, OKAY, THAT MEANS THAT

THERE'S A ONE-IN-10 CHANCE

OF IT RAINING TONIGHT.

THIS IS EQUIVALENT, MEANING

THAT IT'S THE SAME THING,

WHICH ALSO IS EQUIVALENT TO

ONE-TENTH OUT OF ONE,

FROM ZERO TO ONE.

SO, AGAIN, VERY, VERY UNLIKELY

THAT THIS WOULD HAPPEN.

OKAY? VERY UNLIKELY

FOR THERE TO BE RAIN TODAY.

Vanessa holds a sheet of paper that reads, equally likely, 50%, 5/10, 0.5.

She says, SIMILARLY,

IF SHE SAYS THERE'S A 50--

HE OR SHE SAYS THERE'S

A 50% CHANCE OF RAIN TODAY,

WE KNOW THAT

THAT'S EQUALLY LIKELY.

IT MIGHT RAIN

AS MUCH AS IT MIGHT NOT RAIN.

OKAY? SO, IN THIS CASE,

BETTER TO BE SAFE THAN SORRY.

I WOULD BRING AN UMBRELLA

OR A RAIN JACKET,

WHEREVER YOU'RE GOING.

Vanessa holds a sheet of paper that reads, certain, 90%, 9/10, 0.9.

Vanessa continues, AND IF SHE SAID--

OR HE SAID, I SHOULD SAY--

A 90% CHANCE OF RAIN TODAY,

IT'S ALMOST CERTAIN

THAT IT'S GOING TO RAIN.

SO, IN THIS CASE,

I WOULD USE THIS PROBABILITY

TO MAKE A DECISION

AND BRING AN UMBRELLA,

RAIN JACKET, RAIN BOOTS

TO SCHOOL

OR WHEREVER YOU'RE GOING TO PLAY

THAT DAY.

SO, YOU SEE

Vanessa holds up the number line and continues,

FROM OUR NUMBER LINE

THAT PROBABILITY RANGES

FROM ZERO, WHICH MEANS,

WHICH IS-- SORRY--

EXTREMELY UNLIKELY, IMPOSSIBLE.

TO ONE, WHICH IS MEANING

CERTAINLY SOMETHING WILL HAPPEN.

OKAY?

SO, IN THE NEXT SEGMENT,

WHEN WE TALK ABOUT

DIFFERENT GAMES,

WE'RE GOING TO PLOT THIS

AND DIFFERENT SCENARIOS

THAT YOU MIGHT DEAL WITH

ON A DAILY BASIS

ON OUR NUMBER LINE.

LET'S PLAY ONE MORE GAME

BEFORE WE WATCH OUR NEXT SHOW.

I HAVE A DECK OF CARDS HERE.

AND THEY RANGE FROM ACE

ALL THE WAY UP TO 10, AND

THEN WE HAVE THREE FACE CARDS

WITH THE ACE.

SORRY. THREE FACE CARDS.

SO, EACH SUIT HAS 13 CARDS.

WE HAVE THE HEARTS,

THE DIAMONDS, THE SPADES

AND THE CLUBS.

Vanessa shuffles a deck of cards and says,

IF I SAID TO YOU, "WHAT ARE

THE ODDS OF PICKING UP

A SUIT OF HEARTS

OUT OF MY DECK,"

WHAT WOULD THE ODDS BE?

Vanessa puts the formula back onto the display and says,

KNOWING THAT OUR

THEORETICAL PROBABILITY, AGAIN,

IS THE NUMBER

OF FAVOURABLE OUTCOMES--

SO, WE KNOW THAT THERE ARE

13 HEARTS IN OUR DECK.

OVER HOW MANY TOTAL

OR POSSIBLE OUTCOMES ARE THERE.

WE KNOW THAT THERE ARE 52 CARDS

IN THE DECK.

SO, 13 OVER 52

IS OUR FRACTION THAT WE USE,

Vanessa holds up a blue card with the fraction 13/52 on it.

She continues, WHICH IS THE SAME THING

AS ONE OVER FOUR.

SO, WE HAVE

A ONE-OUT-OF-FOUR CHANCE

OF PICKING UP A HEART WHEN I...

...QUICKLY SHUFFLE.

AND I'M GOING TO PICK

THE FIRST CARD ON TOP.

SO, I HAVE

A ONE-OUT-OF-FOUR CHANCE,

WHICH UNFORTUNATELY IS UNLIKELY.

OR MAYBE YOU DON'T WANT

TO PICK A HEART.

THAT'S YOUR FAVOURITE SUIT.

BUT LET'S SAY IT'S UNLIKELY

THAT YOU'RE GOING TO PICK

A HEART, A CARD THAT HAS

THE SUIT OF A HEART IN IT.

COMPARED TO--

THERE'S STILL CLUBS.

THERE'S STILL SPADES.

AND THERE'S STILL DIAMONDS.

SO, YOU'RE MORE LIKELY TO PICK

ONE OF THE OTHER THREE SUITS

THAT ARE REMAINING.

SO, ARE YOU READY TO SEE

IF I CAN PICK A HEART?

Vanessa draws the ace of hearts out of the deck of cards.

She says, OH, MY GOODNESS!

I DID.

(LAUGHING)

OKAY. SO, EVEN THOUGH MY ODDS

WERE UNLIKELY

THAT I WOULD PICK THIS,

ONE OUT OF FOUR,

I WAS STILL ABLE TO DO IT.

SO, THERE'S STILL HOPE OUT THERE

FOR ALL OUR LOTTERY PLAYERS.

ANYWAYS, I WOULD LIKE NOW

JUST TO THROW TO HAMZA,

AND HE IS FROM THE SHOW

LOOK KOOL,

AND HE'S GOING TO GO THROUGH

SOME AWESOME PROBABILITY GAMES,

EXPERIMENTS AND DEFINITIONS

OVER THE COURSE OF

A FEW MINUTES.

I HOPE YOU REALLY ENJOY,

AND I'LL SEE

ALL YOU PROBABILITY LOVERS

HERE AFTER THE VIDEO.

The animated sun rises.

Hamza flips a coin. He is clean shaven with short dark hair.

He wears a navy blue dress shirt and an orange and white striped bow tie.

Hamza says, OKAY.

HEADS.

TAILS? LET'S TRY IT AGAIN.

TAILS.

HEADS?

WHAT ARE THE ODDS I'M EVER

GOING TO GET THIS RIGHT?

TO FIND OUT,

WE'LL MEET A BIG CARD...

A man wearing Jack of Hearts costume enters the room.

(IN FRENCH ACCENT)

The man says, I AM JACQUES DESCARTES.

Hamza says, YEAH. YOU'RE THE ONE I NEEDED

TO WIN GO FISH YESTERDAY.

A clip plays.

...LAUNCH POWERFUL ROCKETS

YOU CAN BUILD AT HOME...

WHOA!

...AND DISCOVER AN UNBELIEVABLE

SCIENTIFIC FACT...

A young girl kneels and puts a microphone to a small white dog’s face.

She says, WHEN'S YOUR BIRTHDAY?

MINE IS NOVEMBER 9TH.

OH. WE HAVE A MATCH.

Hamza says, ...ON

LOOK KOOL.

(Upbeat music plays)

Hamza spins and puts on sunglasses. He wears a blue shirt and a white and blue striped bow tie.

Colorful geometric shapes fall onto a grassy field. The shapes grow to form a colorful city skyline.

(KOOL KATT MEOWING)

Colorful bridges form over a river. A yellow staircase rotates around a red tower.

A purple airplane circles the tower. Koolkatt watches an orange tower rise from the ground.

The title, Look Kool appears over a blue sky.

A coin shoots out of KoolKatt’s toaster-shaped back.

Hamza catches it and says, HEADS.

TAILS AGAIN.

HOW IS THIS POSSIBLE?

THAT'S, LIKE, 10 IN A ROW NOW.

KOOL CAT AND I

ARE PLAYING FLIP THE COIN.

AND SO FAR, HE'S WON EVERY TIME.

(LAUGHING)

MAYBE I NEED SOME OLD FASHIONED

LUCKY CHARMS,

LIKE THIS FOUR-LEAF CLOVER

AND THIS HORSESHOE.

OKAY, OKAY. ONE MORE.

ONE MORE. LET'S GO.

KoolKatt shoots out another coin.

Hamza catches it and says, HEADS.

TAILS AGAIN.

HOW IS THIS POSSIBLE?

THAT'S, LIKE, 10 IN A ROW NOW.

IT LOOKS LIKE

YOU COULD USE SOME HELP.

WHO ARE YOU?

Jacques enters the room.

He says, I AM JACQUES DESCARTES.

PERHAPS YOU REMEMBER ME

FROM YOUR DECK OF CARDS, NO?

Hamza says, YEAH. YOU'RE THE ONE I NEEDED

TO WIN GO FISH YESTERDAY.

NOW YOU DECIDE TO SHOW UP?

Jacques says, AND DO NOT BLAME ME

FOR PROBABILITY.

I DO NOT MAKE THE RULES.

Hamza says, PROBABILITY? WHAT'S THAT?

Jacques says, PROBABILITY IS A TYPE OF MATH

THAT HELPS PREDICT HOW LIKELY

SOMETHING IS TO HAPPEN.

Hamza says, WAIT. YOU MEAN MATH

CAN TELL ME HOW LIKELY IT IS

I'LL GET THE CARD I NEED

IN GO FISH,

OR WIN A COIN TOSS?

Jacques says, UH, YES.

I MEAN, WE CARDS KNOW ABOUT IT,

BUT WE PLAY

GAMES OF CHANCE ALL DAY LONG.

Hamza says, CAN YOU TELL ME

WHY KOOL CAT KEEPS WINNING?

Jacques says, I KNOW EXACTLY WHY KOOL CAT

KEEPS WINNING.

AND MAYBE YOU'LL FIGURE

THAT OUT FOR YOURSELF, EH?

(SNORTING ARROGANTLY)

KoolKatt shakes his head.

Hamza says, OKAY. CAN YOU TELL ME

HOW PROBABILITY WORKS?

Jacques says, OF COURSE.

PROBABILITY IS

THE NUMBER OF OUTCOMES YOU WANT

DIVIDED BY THE NUMBER

OF POSSIBLE OUTCOMES.

Hamza says, OH, OKAY.

SO, I WANT HEADS, AND THERE'S

ONLY TWO POSSIBLE OUTCOMES,

HEADS OR TAILS.

SO, THAT'S ONE DIVIDED BY TWO,

WHICH IS THE SAME AS ONE-HALF.

SO, TECHNICALLY, IT SHOULD BE

ON HEADS HALF THE TIME, RIGHT?

Jacques says, YOU'RE RIGHT.

IT SHOULD.

BUT EVEN WITH MY LUCKY

FOUR-LEAF CLOVER AND HORSESHOE,

KOOL CAT KEEPS WINNING.

Jacques snorts and says, LUCK HAS NOTHING TO DO WITH IT.

An animated 4-leaf clover walks through a field of clovers and says, OH, BOY. I FEEL LUCKY TODAY.

A brown shoe steps on the clover. The clover sticks to the bottom of the shoe, then frees itself.

The clover says, OOH. I SHOULD HAVE BROUGHT

MY LUCKY HORSESHOE.

A horseshoe falls on the clover.

The clover says, OH, MAN.

Hamza says, CAN YOU USE PROBABILITY

TO PREDICT

ANYTHING

OTHER THAN GAMES?

Jacques says, UH, YES, ABSOLUTELY.

I MEAN, PROBABILITY CAN TELL YOU

HOW LIKELY IT IS

THAT YOU'LL FIND A PEARL

IN AN OYSTER.

An animated oyster opens. A pearl is inside it.

Jacques continues, ONE IN 12,000.

OR HOW LIKELY IT IS THAT

A FAMILY WILL HAVE TRIPLETS.

ONE IN 44,000.

A picture of triplets appears.

Jacques continues, OR IT CAN TELL YOU

HOW LIKELY IT IS

THAT A GROWN-UP PERSON

WILL GO TO THE EMERGENCY ROOM

WITH A POGO STICK INJURY.

ONE IN 115,300.

A man hops on a pogo stick, then crashes.

The man says, OW!

Hamza says, SO, PROBABILITY IS AN

EXACT WAY TO LOOK AT THINGS?

Jacques says, UH, IT'S NOT EXACT.

BUT IT DOES SHOW YOU

HOW LIKELY OR UNLIKELY

IT IS TO HAPPEN.

Hamza says, OH, YEAH.

I MEAN, IF SOMETHING'S UNLIKELY,

THAT DOESN'T MEAN

THAT IT'S IMPOSSIBLE.

I MEAN, UNLIKELY THINGS

HAPPEN ALL THE TIME.

(Upbeat woodwind and tuba music plays)

Hamza flies through the sky wearing a pig costume. He flies in formation with several animated pigs.

He sings, NOT UNTIL PIGS FLY

THAT'S WHAT THEY SAY

WHEN SOMETHING'S UNLIKELY

BUT I'M HERE TODAY

FLAPPING MY WINGS

ON THE WAY TO THE SUN

THE ODDS WERE

200 TRILLION BILLION TO ONE

BUT JUST 'CAUSE IT'S RARE

DOESN'T MEAN IT'S NOT DONE

I SAID JUST 'CAUSE IT'S RARE

DOESN'T MEAN IT'S NOT DONE

OINK-OINK-OINK, OINK-OINK-OINK

OINK-OINK-OINK

SOMETIMES A RIVER

IS BACKWARDS FLOWING

SOMETIMES

A TURTLE IS NOT SO SLOWING

SOMETIMES IN SUMMER

IT STARTS SNOWING

AND NOW THAT

YOU'RE ALL KNOWING

I REALLY MUST BE GOING

OINK-OINK-OINK, OINK-OINK-OINK

OINK-OINK-OINK

Hamza says, SO, DO YOU THINK

KOOL KATT WINNING

10 TIMES IN A ROW

IS JUST PURE LUCK?

Jacques says, HA! I THINK

THAT'S AWFULLY IMPROBABLE.

Hamza says, YEAH. ME, TOO.

SO, WHAT ELSE CAN YOU TELL ME

ABOUT PROBABILITY?

Jacques says, OH, HERE IS ONE OF

MY FAVOURITE THINGS.

A graphic appears showing 23 human figures.

Jacques continues, IF YOU HAVE A ROOM OF 23 PEOPLE,

THERE IS A ONE IN TWO CHANCE

THAT TWO OF THEM

WILL HAVE THE SAME BIRTHDAY.

A box appears around two figures.

Hamza says, NOW, THAT DOESN'T

SOUND RIGHT.

I MEAN, THERE'S 23 PEOPLE

AND 365 DAYS IN A YEAR.

Jacques says, I DEAL IN PROBABILITY.

I KNOW WHAT I AM TALKING ABOUT.

Hamza says, OKAY, OKAY.

NO OFFENCE, MONSIEUR.

BUT I THINK I'M GOING TO

HAVE THE INVESTIGATORS

CHECK THIS OUT.

Jacques says, WELL, SUIT YOURSELF.

An animated KoolKatt looks through a magnifying glass.

An announcer says, INVESTIGATION.

A young boy and girl appear on a screen.

Hamza says, HI, INVESTIGATORS.

The kids say, HI, HAMZA.

Hamza says, ALEXANDRA, ETHAN,

I HAVE A QUESTION FOR YOU.

A TYPICAL YEAR

HAS 365 DAYS, RIGHT?

Alexandra and Ethan say, YEAH.

RIGHT.

Hamza says, SO, HOW MANY DIFFERENT

BIRTHDAY DATES

COULD THERE BE IN THE YEAR?

Alexandra and Ethan say, 365?

Hamza says, EXACTLY. SO, HOW MANY

PEOPLE DO YOU THINK

YOU'D HAVE TO ASK

BEFORE YOU'D FIND TWO

WITH THE SAME BIRTHDAY?

Alexandra says, WELL, I THINK WE SHOULD

DIVIDE IT IN TWO,

'CAUSE WE NEED

TWO PERSONS.

Ethan says, OR 185?

Alexandra says, YEAH, ABOUT THAT.

Hamza says, YOU KNOW, I THINK IT

WOULD TAKE A LOT OF PEOPLE, TOO.

BUT I HAVE A BUDDY HERE WHO

THINKS YOU'D NEED A LOT LESS.

LET'S TEST IT.

ASK PEOPLE THEIR BIRTHDAYS

UNTIL YOU FIND A MATCH.

Ethan says, WE'RE ON IT.

The kids approach a group of people outside a large grey brick and stone building.

Ethan says, WE'RE DOING A TV SHOW

ON PROBABILITY,

AND WE'RE WONDERING

WHAT YOUR BIRTHDAY IS.

A woman says, THE 14TH OF FEBRUARY.

Alexandra asks, AND WHAT'S

YOUR BIRTHDAY?

A woman says, MARCH 24TH.

Alexandra kneels beside the small white dog and holds a microphone to its face. She asks, WHEN'S YOUR BIRTHDAY?

COME ON, TELL ME.

The dog’s male owner says, HE ONLY

SPEAKS FRENCH.

Alexandra says, OH.

A line graph appears.

A computerized voice says,

ACCORDING TO THE LAWS

OF PROBABILITY,

IN A ROOM WITH 23 PEOPLE,

IT'S MORE THAN 50% CERTAIN

THAT AT LEAST TWO

WILL HAVE THE SAME BIRTHDAY.

WITH 30 PEOPLE IT'S 75%,

AND WITH 70 IT'S 99%.

BY DOING LOTS OF EXPERIMENTS

LIKE THESE,

WE CAN SEE THAT THE LAWS

OF PROBABILITY WORK.

Ethan holds a microphone up to a woman and asks, AND YOU?

The woman says, MAY THE 18TH.

Several women answer Alexandra and Ethan, MAY 26TH.

SEPTEMBER 6TH.

FEBRUARY 22ND.

AUGUST 28TH.

MAY THE 18TH.

Ethan says, WE GOT TWO.

Hamza says, WOW!

Alexandra says, ALL RIGHT.

THANK YOU.

Hamza asks, HOW MANY DID IT TAKE?

Alexandra counts checkmarks on a grid and counts, ONE, TWO, THREE,

FOUR, FIVE, SIX,

SEVEN, EIGHT, NINE,

10, 11, 12, 13.

Ethan says, JUST 13.

Alexandra says, YEAH. A LOT LESS

THAN WE THOUGHT.

Hamza says, THAT'S A LOT LESS

THAN WE BOTH THOUGHT.

WE'LL CATCH UP

WITH THE INVESTIGATORS LATER.

BUT THE PROBABILITY THAT

I'M BLOWN AWAY BY THIS IS 100%.

Jacques says, AHA!

I KNEW HE'D SEE IT MY WAY.

Hamza continues, PROBABILITY SAYS THAT

A COIN SHOULD LAND HEADS

HALF THE TIME, RIGHT?

SO, MAYBE

I'LL JUST STICK TO HEADS,

AND MAYBE KOOL CAT'S COIN

WILL LAND ON HEADS

A BUNCH OF TIMES IN A ROW.

Koolkatt shakes his head.

Jacques says, AH, EXCUSEZ-MOI.

HOLD YOUR HORSES.

UH, YOU'VE FALLEN FOR

THE MONTE CARLO FALLACY.

Jacques plays Go Fish with KoolKatt.

Jacques says, UH--

GO FISH.

Hamza says, THE MONTE CARLO

WHAT-ACY?

Jacques says, FALLACY. IT'S WHEN

SOMETHING IS NOT TRUE.

IN THIS PARTICULAR CASE,

IT IS THE IDEA THAT

IF YOU'VE HAD BAD LUCK,

YOUR LUCK

HAS TO CHANGE.

THE PROBABILITY OF FLIPPING

A COIN TO TAILS 10 TIMES IS--

IT'S SMALL.

BUT THE PROBABILITY

OF EACH INDIVIDUAL FLIP

IS THE EXACT SAME

EVERY TIME YOU FLIP IT.

DO YOU HAVE ANY THREES?

Koolkatt shakes his head.

Hamza says, I GUESS I STILL HAVE A LOT MORE

TO LEARN ABOUT PROBABILITY.

(Upbeat music plays)

Panels of a puzzle shift and become a picture of Koolkat.

A graphic of a cat head with ears inside it appears.

An announcer says, BRAIN BENDER

Hamza says, TODAY'S PUZZLE-SOLVERS

ARE EVAN AND ALYSSA.

HELLO.

Evan and Alyssa wave and say HI, HAMZA.

HI.

Hamza says, OUR BRAIN-BENDER

IS GOING TO BE A BIT DICEY.

YOU SEE A PAIR OF DICE,

RIGHT?

The kids say, YEAH.

Hamza says, THERE ARE 12 CUPS.

EACH CUP REPRESENTS A NUMBER YOU

COULD ROLL WITH A PAIR OF DICE.

HERE'S THE BRAIN-BENDER.

IF YOU ROLL A PAIR OF DICE

A LOT OF TIMES,

WHICH OF THESE 12 NUMBERS

DO YOU THINK

YOU'LL GET MOST OFTEN?

Evan says, FIVE. FOUR, MAYBE.

Hamza says, WELL,

LET'S FIND OUT.

Evan rolls the dice and says, FOUR.

He drops a token into a red and white cup labelled with the number 4.

Alyssa rolls the dice and says, SIX.

She drops a token into a cup labelled with the number 6.

Evan rolls the dice and says, SEVEN. THERE.

Alyssa rolls the dice and says, 10.

She rolls again and says, SEVEN.

SIX AND SEVENS

ARE IN THE LEAD.

The kids roll the dice repeatedly.

Hamza says, IT LOOKS LIKE THEY'RE ON A ROLL.

WE'LL CHECK BACK WITH THEM

LATER.

(BRAKES SQUEALING)

An animation shows blue and yellow KoolKatts racing down a street.

The announcer says, CHALLENGE.

Hamza stands in a park with two teams of one boy and one girl wearing yellow or blue shirts.

He says, WELCOME TO THE

LOOK KOOL

PROBABILITY CARNIVAL.

AND TO MY RIGHT, I HAVE KIKI

AND ZACHARY. TEAM YELLOW.

Kiki and Zacahry say, TEAM YELLOW.

Hamza continues, AND ON MY LEFT, I HAVE

ELENI AND DONATO. TEAM BLUE.

Eleni adn Donato says, TEAM BLUE.

Hamza and the kids approach a game with several picture of KoolKatt wearing a clown hat and nose.

Hamza says, FIRST UP, WE HAVE

THE BALL TOSS.

BUT BE WARNED.

ONE OF THESE CLOWNS

IS THE DREADED CLOWN OF DOOM.

A red mannequin head wears a colorful clown wig.

(EVERYONE GASPING)

Hamza says, MM-HMM. WHOEVER KNOCKS IT OVER

WILL FACE DIRE CONSEQUENCES.

ZACHARY, YOU GET TO GO FIRST.

He throws a ball through one of the KoolKatt pictures. Text over the clown head reads, safe.

Hamza says, OOH. LET'S TAKE A CLOSER LOOK AT

THIS WITH MY MIND'S EYEGLASSES.

Hamza puts on glasses.

A computerized voice says,

NOW THAT ONE OF

THE EIGHT CLOWNS

HAS BEEN ELIMINATED,

THE PROBABILITY OF HITTING

THE CLOWN OF DOOM

BECOMES ONE IN SEVEN.

Hamza removes the glasses and says, WHOA!

NOW IT'S TEAM BLUE'S TURN.

Kids take turns throwing balls at the wall of KoolKatt pictures.

Hamza says, YES.

WOO-HOO-HOO!

The computerized voice says, WITH EVERY SAFE SHOT,

THE DANGER INCREASES.

THE PROBABILITY

IS NOW ONE IN FIVE.

ALL RIGHT, DONATO.

Kids take turns throwing balls at the wall of KoolKatt pictures.

Hamza says, OOH.

KEANA, THE PROBABILITY IS?

Keana says, ONE OUT OF TWO.

Hamza says, ONE OF THESE IS

THE CLOWN OF DOOM.

LET'S FIND OUT WHICH ONE IT IS.

Keana throws a ball and knocks over a picture.

Hamza says, WOO-HOO-HOO!

DONATO, WHAT DO YOU THINK

IS THE PROBABILITY THAT

THAT IS THE CLOWN OF DOOM?

Donato says, ONE OUT OF ONE.

Hamza says, I'M PRETTY SURE

YOU'RE RIGHT.

Donato throws a ball at the last picture. It flips over revealing a picture of a clown.

(SIREN WAILING)

Hamza says, OH! THERE IT IS.

Donato says, UH-UH.

Water sprays Donato from the mouth of the red mannequin head.

He falls over laughing and says, UGH!

Hamza says, WELL, I THINK THE

PROBABILITY OF THIS CHALLENGE

GETTING WETTER IS REALLY HIGH

WHEN WE GET BACK.

Two red water balloons pop.

(EVERYONE CHEERING)

Hamza flips a coin and says, OH, HEADS. IF IT'S HEADS HALF

THE TIME I FLIP THE COIN,

HOW COME KOOL CAT KEEPS WINNING?

OH, WELL. LET'S SEE HOW

THE BRAIN-BENDER IS GOING.

Hamza approaches the screen and waves his hand.

Evan says, THE LAST ROLL

OF THE GAME IS...

Evan rolls the dice.

Evan and Alyssa say, ...FIVE.

Evan drops a token into a cup

He says, OH.

Hamza says, OKAY. IT'S TIME TO COUNT UP

HOW MANY TOKENS ARE IN EACH CUP.

Evan and Alyssa take tokens out of the cups and count,

12, WE HAVE FOUR.

SIX, 10.

THREE, SEVEN AND EIGHT.

WOW. WE GOT A LOT.

15.

IN SIX WE HAVE 13.

IN FIVE WE HAVE SEVEN.

FOUR, FIVE. SIX.

IN TWO, WE ONLY HAVE ONE.

AND IN ONE, NOTHING.

Evan says, YOU KNOW, IT'S ACTUALLY

IMPOSSIBLE TO GET A ONE,

BECAUSE THERE'S TWO DICE.

Hamza says, SO, TELL ME WHICH ONE

ACTUALLY HAD THE MOST.

The kids say, SEVEN.

Hamza says, DO YOU KNOW WHY?

Evan says, NO.

Hamza says, WHY DO YOU THINK

THEY CALL IT

LUCKY NUMBER SEVEN?

Evan says, MAYBE BECAUSE SEVEN ALWAYS WINS.

Alyssa says, A REALLY GOOD ANSWER,

I THINK.

Hamza says, PROBABLY.

THANKS, EVAN. THANKS, ALYSSA.

Evan and Alyssa wave and say, BYE, HAMZA.

BYE.

Evan rolls two yellow and orange dice and says,

THERE YOU GO. SEVEN.

I'M GOING TO SEE IF THERE'S

A MATHEMATICAL EXPLANATION

BEHIND "LUCKY SEVEN."

IF I HAVE TWO DICE,

HOW MANY DIFFERENT WAYS

CAN I ROLL SEVEN?

The animation of KoolKatt breaks into multiple pieces then reforms whole.

The announcer says, DECONSTRUCT.

Hamza says, DECONSTRUCT.

WHOA.

The dice float in mid air, rotating into various combinations of seven.

Hamza says, ARE YOU SEEING WHAT I'M SEEING?

THERE ARE A LOT OF POSSIBLE

COMBINATIONS TO MAKE SEVEN.

A graphic appears showing all possible dice combinations.

Hamza says, OH, AND LOOK.

THERE'S A PATTERN

TO THE COMBINATIONS.

THERE'S ONE WAY TO MAKE TWO,

TWO WAYS TO MAKE THREE,

THREE WAYS TO MAKE FOUR,

FOUR WAYS TO MAKE FIVE,

FIVE WAYS TO MAKE SIX,

AND SIX WAYS TO MAKE SEVEN.

THE NUMBER OF POSSIBILITIES

INCREASES BY ONE

UNTIL YOU GET

TO SEVEN.

AND THEN IT DECREASES

FOR EVERY NUMBER AFTER THAT

UNTIL YOU GET TO 12.

HEY, IT MAKES A TRIANGLE.

SO, "LUCKY SEVEN"

IS ACTUALLY JUST

THE MOST LIKELY NUMBER

THAT YOU CAN ROLL WITH TWO DICE.

IT'S NOT REALLY LUCK AT ALL.

The 4-leaf clover walks and smiles.

He says, OH, BOY. I FEEL LUCKY TODAY.

UH-OH.

(THUNDER CRASHING)

Rain falls on the clover, then lightning strikes it.

The clover lies on the ground and says, WELL, I GUESS I SHOULDN'T HAVE

CARRIED THIS BIG HUNK OF METAL

IN A THUNDERSTORM.

OH, NO.

Lightning strikes the horseshoe. The horseshoe falls on the clover.

The clover says, OH, MAN.

The animated KoolKatt looks through the magnifying glass.

The announcer says, INVESTIGATION.

A woman says, MY BIRTHDAY IS NOVEMBER 21ST.

Ethan and Alexandra chase after a pigeon.

They yell, WHEN'S YOUR BIRTHDAY?

NO, DON'T GO. WAIT!

A man says, NOVEMBER 16TH.

Ethan says, AND YOU?

Several people respond, NOVEMBER 9TH.

10TH OF MARCH.

22ND OF NOVEMBER.

MINE IS NOVEMBER 9TH.

Alexandra says, OH, WE HAVE A MATCH.

Hamza says, OKAY.

HOW MANY PEOPLE DID IT TAKE

TO GET A BIRTHDAY MATCH

THIS TIME?

Alexandra says, 37.

THAT'S NOT A LOT...

Ethan says, ...COMPARED TO

WHAT WE THOUGHT.

Alexandra says, YEAH. 180 COMPARED TO 37?

THAT'S NOTHING.

Hamza says, NEITHER TRY TOOK 180 PEOPLE.

Ethan and Alexandra say,

NO.

NOT EVEN CLOSE.

The line graph appears.

The computerized voice says, THE PROBABILITY

OF FINDING A MATCH

AFTER ASKING 13 PEOPLE

IS ONLY 19%.

THAT IS SOMEWHAT UNLIKELY.

THE PROBABILITY

OF FINDING A MATCH

AFTER 37 PEOPLE IS 85%.

VERY LIKELY.

AFTER ASKING ONLY 60 PEOPLE,

YOU ARE ALMOST CERTAIN

TO HAVE A MATCH.

Hamza says, THE NUMBER OF PEOPLE

IS A LOT LOWER

THAN WE THOUGHT.

READY TO DO

SOME ROCKET SCIENCE NOW?

Ethan says, YEAH.

Alexandra says, OH, YEAH. BIG TIME.

The animated sun rises.

Vanessa says, WELCOME BACK.

I HOPE YOU ENJOYED THE VIDEO.

The caption reads, Junior 4-6. Teacher Vanessa.

She continues, WE'RE GOING TO TALK ABOUT

THE ODDS

OF MULTIPLE EVENTS HAPPENING.

SO, YOU SEE TO MY RIGHT HERE,

OR YOUR LEFT,

THREE DIFFERENT SPINNERS.

AND WE HAD JUST TALKED ABOUT

THEORETICAL PROBABILITY

BEING THE NUMBER OF

LIKELY EVENTS

OVER THE TOTAL POSSIBILITY

OF EVENTS THAT COULD HAPPEN.

SO, IF WE LOOK FIRST

ON THIS SPINNER,

IF I WANTED TO LAND ON

ONE OF THE SIDES OF THE SPINNER,

I'D HAVE A PROBABILITY

OF ONE OVER TWO.

OKAY? SO, I COULD EITHER LAND

HERE OR I COULD LAND HERE.

Vanessa points at a circle divided into two sections.

She continues, THAT MEANS I HAVE

AN EQUALLY LIKELY PROBABILITY

THAT I'D LAND ON THE BLUE SIDE

Vanessa colors half the circle blue.

COMPARED TO LANDING ON

THE WHITE SIDE.

EQUALLY LIKELY.

IN THE MIDDLE SPINNER, I HAVE

ONE, TWO, THREE, FOUR SECTIONS.

SO, THE ODDS OF ME LANDING ON

ANY ONE OF THOSE FOUR SECTIONS

IS ONE OUT OF FOUR.

AND ON THE SPINNER HERE,

WE SEE THAT WE HAVE

ONE, TWO, THREE, FOUR,

FIVE, SIX.

SO, THE LIKELIHOOD OF ME LANDING

ON ANY ONE OF THOSE SECTIONS

OF THE SPINNER IS ONE OVER SIX.

OKAY? SO, AS YOU SEE,

YOUR ODDS OF LANDING ON

ANY ONE SECTION

GET SMALLER, EVEN THOUGH

THE FRACTION GETS BIGGER.

THE PERCENT GETS SMALLER

AS YOU HAVE MORE SECTIONS ADDED.

Vanessa removes the drawings of circular spinners from the tabletop display.

A new sheet reads, Red twice in a row: 1/4 x 1/4.

Vanessa continues, SO, WHAT HAPPENS IF ONE OF

YOUR FRIENDS AND YOURSELF

PLAY A GAME,

AND YOU ARE SPINNING

A WHEEL,

AND YOU HAVE FOUR SECTIONS.

AND THE WAY TO WIN IS IF

YOU LAND ON RED TWICE IN A ROW.

WHAT ARE YOUR ODDS

OF WINNING THE GAME?

OKAY?

SO, WE KNOW THAT WE HAVE

A ONE-OUT-OF-FOUR PROBABILITY

OF WINNING,

BECAUSE WE KNOW WE HAVE ONE RED

OUT OF A TOTAL OF FOUR.

OKAY? SO, AFTER ONE SPIN,

THAT'S THE PROBABILITY.

WHAT ARE THE ODDS

THAT YOU CAN GET IT TWICE?

SO, ON YOUR SECOND SPIN,

YOU AGAIN HAVE

A ONE-OUT-OF-FOUR PROBABILITY

OF YOU SPINNING A RED.

IN TOTAL,

TO FIND OUT WHAT OUR PROBABILITY

WOULD BE

FOR THESE TWO EVENTS HAPPENING

AFTER EACH OTHER,

WE CAN MULTIPLY

THE TWO FRACTIONS TOGETHER.

SO, WHEN WE MULTIPLY FRACTIONS,

WE LOOK TO MULTIPLY

THE NUMERATORS.

ONE TIMES ONE IS ONE.

AND WE PUT IT OVER

THE DENOMINATOR.

SO, WE MULTIPLY THOSE TWO

TOGETHER.

FOUR TIMES FOUR IS 16.

Vanessa writes the fraction 1/16.

She says, SO, MY ODDS OF ROLLING RED

TWICE IN A ROW

ON THIS WHEEL

ARE ONE OUT OF 16.

NOW, IF I'M PUTTING THAT ON

MY NUMBER LINE,

I KNOW THAT IT WOULD BE

ALMOST BETWEEN

IMPOSSIBLE AND UNLIKELY.

OKAY?

Vanessa points at the number line.

She says, SO, THIS IS A HARD GAME TO WIN,

TO GET TO ROLL--

OR TO SPIN RED TWICE IN A ROW.

BUT LET ME TRY, 'CAUSE I THINK

I WAS LUCKY ON THAT OTHER.

(LAUGHING)

THAT OTHER GAME.

I WAS PICKING A HEART. OKAY.

Vanessa spins the 4-colored lazy Susan wheel.

SO, UNFORTUNATELY, NO.

I ROLLED WHITE.

AND I ROLLED WHITE AGAIN.

SO, I WOULD NOT HAVE WON

ON MY GAME.

THE ODDS OF ME LOSING, THEN,

WOULD BE--

SO, THIS IS FOR A WIN.

AND THEN WE KNOW THAT

MY ODDS OF LOSING

WOULD BE 15 OUT OF 16.

SO, MUCH HIGHER

THAT I WOULD'VE LOST.

BECAUSE WE KNOW 15 OVER 16

PLUS ONE OVER 16

GIVES ME 16 OVER 16, OR A WHOLE.

OKAY? SO, UNFORTUNATELY,

I DIDN'T WIN THAT GAME.

Vanessa reveals a new sheet of paper on the display that reads, 3 heads in a row: 1/2 x 1/2 x 1/2

Vanessa continues, NOW, WHAT IF SOMEONE SAYS,

"CAN YOU FLIP A COIN

"SO THAT YOU GET HEADS

THREE TIMES IN A ROW?"

WELL, WHAT'S THAT PROBABILITY?

SO, ON THE FIRST ROLL,

I HAVE A ONE-IN-TWO SHOT,

BECAUSE WE TALKED ABOUT

HEADS OR TAILS

BEING THE TWO POSSIBILITIES,

AND WE SAID WE WANTED HEADS,

OKAY?

SO, THAT WOULD BE MY FIRST ROLL,

MY FIRST FLIP.

MY SECOND FLIP,

I HAVE THE SAME PROBABILITY.

AND MY THIRD FLIP, I HAVE TO GET

A ONE-OUT-OF-TWO SHOT

OF GETTING A HEAD.

WHAT IS THAT ALTOGETHER?

SO, WE CAN MULTIPLY

OUR FRACTIONS.

ONE TIMES ONE TIMES ONE,

YOU GET ONE.

OVER-- NOW, WE MULTIPLY

OUR DENOMINATORS TOGETHER.

TWO TIMES TWO IS FOUR.

TIMES TWO AGAIN IS EIGHT.

Vanessa writes the fraction 1/8.

She says, SO, I HAVE A ONE-OUT-OF-EIGHT

PROBABILITY

OF FLIPPING A COIN AND

RECEIVING HEADS, THREE IN A ROW.

THREE TIMES IN A ROW.

AGAIN, WE'RE LOOKING AT

THE "UNLIKELY" RANGE.

UM, SOMEWHERE IN BETWEEN HERE.

OKAY? SO, YOUR FRIEND

IS MORE LIKELY TO WIN

IF THEY SAID THAT

THEY COULD ROLL ANYTHING

BUT THREE HEADS IN A ROW.

IF THEY SAID THAT THEY COULD

ROLL EITHER A HEADS OR TAILS?

(LAUGHING)

AH, THAT WOULD BE SMART.

OKAY. SO, LET'S SEE IF I CAN

ROLL THREE HEADS IN A ROW.

Vanessa flips a coin and says,

ONCE, AND I PROMISE

I'M NOT CHEATING.

CAN YOU SEE THE REFLECTION?

OKAY.

She flips the coin again and says, NO. I GOT A TAIL.

OKAY? SO, I DIDN'T WIN AGAIN.

AND HOW DO WE KNOW THAT

IT WAS GOING TO BE DIFFICULT

FOR ME TO WIN THIS GAME?

BECAUSE WHEN WE PLOT IT

ON OUR NUMBER LINE,

WE SEE THAT ONE OUT OF EIGHT

IS A VERY SMALL FRACTION,

LESS THAN UNLIKELY.

SO, THAT GAME WOULD BE

VERY, VERY DIFFICULT TO WIN.

LET'S PLAY ONE MORE BEFORE

WE WATCH OUR NEXT EPISODE

OF

MATHXPLOSION.

Vanessa picks up a deck of cards and places a blue card with the fraction 26/52 on the display.

Vanessa says, UM, LET'S SEE IF I CAN

GET THESE ODDS HERE.

SO, WHAT DO YOU THINK

I'M GOING TO--

HOW CAN I WIN THIS GAME?

LET'S SAY I CAN PICK EITHER

TWO OF TWO DIFFERENT SUITS,

OR I COULD PICK, UM,

ONE RED CARD.

OKAY? SO, I KNOW THAT THERE ARE

26 RED CARDS IN THIS DECK.

AND THERE'S 26 BLACK CARDS

IN THIS DECK,

SO IT'S EQUALLY LIKELY THAT

I WOULD PICK A RED OR A BLACK.

SO, MY CHANCES ARE RIGHT IN

THE MIDDLE OF THAT NUMBER LINE,

THAT 0.5, OR ONE OVER TWO.

UM, LET'S GO THIS WAY.

ACTUALLY, NO. LET'S TRY IT.

LET'S DO IT THIS WAY AGAIN.

OKAY. SO, LET'S SEE MY ODDS OF

PICKING A BLACK CARD

ON THE TOP OF MY PILE.

Vanessa picks the 8 of hearts out of the deck.

Vanessa says, AND IT WAS A RED.

SO, UNFORTUNATELY, I DID NOT WIN

THE GAME

THAT I WOULD HAVE WON

IF I HAD DRAWN A BLACK CARD.

SO, I WAS EQUALLY LIKELY

TO WIN AND LOSE,

AND UNFORTUNATELY,

I TAKE THE LOSS ON THIS ONE.

SO, I WOULD LOVE FOR YOU TO

WATCH THIS NEXT EPISODE

OF

MATHXPLOSION.

IT'S GOING TO TEACH YOU

HOW SOCKS AND MATH TOGETHER

ARE AN AWESOME, AWESOME

MAGIC TRICK.

SO, CHECK IT OUT, AND I'LL

MEET YOU HERE AFTER THE VIDEO.

The animated sun rises.

(laser sounds)

Kids sing, WHAT A HIT

IT'S NOT A TRICK

IT'S

MATHXPLOSION

The MathXplosion logo appears.

The kids sing, JUST FOR YOU, COOL AND NEW

MATHXPLOSION

A brown-haired man with a neatly trimmed beard, carries a brown wooden drawer full of colorful socks.

He wears a red t-shirt with the MathXplosion logo on it.

The man says, DID YOU KNOW THAT I CAN FIND

TWO SOCKS OF THE SAME COLOUR

IN THIS MESSY SOCK DRAWER

WITH MY EYES CLOSED?

YEP, THAT'S RIGHT.

AND AS AMAZING

AS THAT SOUNDS ALREADY,

I NEED TO PICK

JUST FOUR SOCKS TO DO IT.

I'LL SHOW YOU HOW IT'S DONE.

YOU WON'T BELIEVE YOUR EYES.

The man opens the drawer. It is empty.

The man says, NEED SOME SOCKS, PLEASE.

GET SOME SOCKS.

The man stands behind a table.

I HAVE BEFORE ME

A DRAWER FULL OF SOCKS.

THESE SOCKS COME IN

THREE DIFFERENT COLOURS.

WE HAVE BLUE, GREEN AND PINK.

THE TOTAL NUMBER OF SOCKS

IN THE DRAWER

DOESN'T MATTER AT ALL,

AS LONG AS I KNOW

HOW MANY COLOURS THERE ARE.

IN THIS CASE, THREE COLOURS.

SO, WHAT I'M GOING TO DO IS

PULL JUST FOUR SOCKS

FROM THE DRAWER IN THE DARK.

AND I CAN GUARANTEE

THAT AT LEAST TWO

WILL BE OF THE SAME COLOUR.

LET'S TURN OFF THESE LIGHTS.

(CLAPPING)

GREAT. OH, BOY. THAT'S DARK.

(CAT YOWLING)

OH, SORRY, KITTY.

OKAY.

YOU KNOW, THIS IS WAY TOO DARK.

THIS ISN'T WORKING.

LET'S TURN THE LIGHTS BACK ON.

(CLAPPING)

LIGHTS?

(CLAPPING)

OH.

WELL, THAT DIDN'T WORK AT ALL.

(CHUCKLING)

I KNOW.

I'LL DO THIS BLINDFOLDED.

OKAY.

The man puts on a blindfold, then reaches into the drawer and pulls out socks.

He says, ONE, TWO, THREE.

ANY MATCHING COLOURS YET?

NO?

OKAY.

WELL, KEEP YOUR EYE ON

SOCK NUMBER...

...FOUR.

The man pulls out a second pink sock and says,

YES.

THE FIRST THREE SOCKS

WERE DIFFERENT COLOURS,

SO THE FOURTH ONE

HAS

TO MATCH.

IF YOU START WITH

THREE SOCK COLOURS,

PICKING FOUR SOCKS

GUARANTEES AT LEAST TWO SOCKS

OF THE SAME COLOUR.

AMAZING.

The man draws a yellow circle on a chalkboard, then taps the circle with his fist. The chalkboard becomes a monitor showing an animation of socks floating out of a dresser drawer.

The man says, THE LIKELIHOOD OF SOMETHING

HAPPENING,

LIKE CHOOSING

A SPECIFIC SOCK COLOUR,

IS CALLED PROBABILITY.

YOU CAN USE

THE SAME TRICK ON MITTENS, TOO.

TO GUARANTEE THAT YOU

FIND TWO MITTENS

OF THE SAME COLOUR IN THE DARK,

THE NUMBER OF MITTENS TO PICK UP

IS THE NUMBER OF MITTEN COLOURS

PLUS ONE.

THREE COLOURS, FOUR MITTENS.

Four mittens float above the dresser.

The man says, SO, THERE YOU HAVE IT.

I'VE SHARED YET ANOTHER

AMAZING SECRET:

HOW TO MATCH UP SOCKS

IN THE DARK.

TRY IT OUT YOURSELVES AT HOME.

BUT REMEMBER, USE CLEAN SOCKS.

(SNIFFING)

NOT SMELLY ONES.

PROBABILITY.

IT'S NOT MAGIC; IT'S MATH.

The drawer is full of socks. The Math Xplosion logo appears.

Text reads, produced by GAPC Entertainment. In association with TVO Kids. With the financial participation of Bell Fund, Canadian Media Fund and Shaw Rocket Fund.

The animated sun rises.

Vanessa says, WELCOME BACK.

LET'S PUT IT ALL TOGETHER NOW.

REVIEWING OUR DEFINITION

OF PROBABILITY,

THE LIKELIHOOD

OF SOMETHING HAPPENING.

WE'VE SHOWN IT THROUGH

A FRACTION AND NUMBER LINE.

AND WE USE PROBABILITY TO

MAKE DECISIONS AND PREDICTIONS,

ESPECIALLY THE WEATHER.

SO, THIS IS THE TIME FOR YOU

TO GET INVOLVED.

IF YOU HAVE THOSE MARKERS

AND THAT PAPER

AND DIFFERENT FORMS OF

PROBABILITY GAMES,

I WOULD LOVE FOR YOU

TO GET THAT READY

AND BRING IT TO YOUR WORK AREA.

AND WE ARE GOING TO

PLAY A LITTLE GAME.

SO, YOU, ON A PIECE OF PAPER,

WILL WRITE PROBABILITY EVENTS

THAT COULD HAPPEN IN WORDS.

OKAY?

SO, FOR EXAMPLE...

Vanessa places a green card on the tabletop display. It reads, “I win the lottery”.

Vanessa continues, ...MY FIRST POSSIBLE EVENT

THAT COULD HAPPEN?

I WIN THE LOTTERY.

OKAY? SO, I'M PICKING AN EVENT

THAT COULD HAPPEN.

AND THEN,

WHAT I'M GOING TO DO IS

THINK ABOUT THE LIKELIHOOD

OF IT OCCURRING. OKAY?

SO, YOU COULD THEN EXCHANGE

YOUR EVENT WITH A FRIEND,

MAYBE WITH A PARENT.

MAYBE TALK TO, UM,

ANOTHER ADULT IN YOUR LIFE,

LIKE A TEACHER.

ASK THEM WHAT ARE THE ODDS THAT

THEY'RE GOING TO WIN THE LOTTERY

THIS WEEK, AND THEN

PLOT IT ON YOUR NUMBER LINE.

Vanessa holds up the number line.

She continues, SO, IF I SAID TO MY TEACHER,

"MISTER OR MISS,

WHAT ARE THE ODDS

THAT YOU'RE GOING TO WIN

THE LOTTERY THIS WEEK?"

YOU CAN TELL THEM THAT,

IF THEY'RE UNSURE,

THAT IT WOULD BE SOMEWHERE

IN THIS RANGE

THAT THEY WIN THE LOTTERY.

OKAY? SO, THIS EVENT,

WE KNOW THAT OCCURS--

ONE OUT OF 33,000,000

ARE THE ODDS

OF WINNING THE LOTTERY.

SO, VERY, VERY UNLIKELY

THAT YOU WIN THE LOTTERY.

YOU COULD COME UP WITH

ANOTHER EVENT

THAT YOU COULD ASK YOUR FRIEND

MIGHT HAPPEN.

YOU FLIP A COIN

AND YOU LAND ON TAILS.

NOW, KNOWING WHAT YOU DO

ABOUT PROBABILITY,

YOU KNOW THAT YOU HAVE

AN EQUALLY LIKELY PROBABILITY,

ONE OVER TWO, BECAUSE TAILS--

THERE'S EITHER HEADS OR TAILS

AS THE POSSIBLE OUTCOMES,

AND YOU LAND ON TAILS.

SO, YOU'RE EQUALLY LIKELY, 50%.

AND THEN, WITH YOUR FRIEND

OR YOUR GUARDIAN OR PARENT,

THEY COULD PLOT THIS

ON THE NUMBER LINE.

I FLIP A COIN AND LAND ON TAILS.

NOW, YOU MIGHT WANT TO GET

SOME CERTAIN ONES IN THERE, TOO.

WE ALL ARE HOPING FOR THIS:

SUMMER WILL COME.

SO, YOU MAKE THAT EVENT

ON A PIECE OF PAPER.

YOU WRITE IT DOWN,

AND YOU ASK YOUR FRIEND,

"WHERE CAN IT BE PLACED

ON THE NUMBER LINE?"

IS THAT IMPOSSIBLE,

EQUALLY LIKELY, OR CERTAIN?

AND WE KNOW CERTAINLY,

EVERY SEASON

COMES WITHIN THE YEAR.

SO, IT'S CERTAIN THAT

THE SUMMER WILL COME,

AND THAT SUMMER BREAK

IS INEVITABLE.

OKAY? SO, WHAT WE'RE PRACTISING

WHEN WE DO THIS GAME,

WE'RE TALKING ABOUT

THE PROBABILITY

OF LIFE EVENTS HAPPENING.

AND ON OUR NUMBER LINE,

WE'RE PLOTTING THEM ON A SCALE

BETWEEN ZERO, HALF, AND ONE

AS OUR BENCHMARK NUMBERS.

OKAY? SO, THIS IS GETTING US

IN THE FRAME OF MIND

OF USING THESE TERMS

THAT WE'RE TALKING ABOUT,

PROBABILITY OF EVENTS.

Vanessa puts a green card on the display that reads, viewers are in grades 4, 5, and 6!

Vanessa says, OUR VIEWERS HERE

ARE IN GRADES 4, 5 AND 6.

THAT IS ALMOST CERTAIN.

OUR KEY DEMOGRAPHIC

FOR THIS VIDEO,

THE CURRICULUM,

IS IN THE JUNIOR GRADES.

SO, ALMOST CERTAINLY,

MANY OF OUR VIEWERS ARE--

MOST OF OUR VIEWERS

ARE, UM, IN THOSE GRADES.

BETWEEN LIKELY AND CERTAIN.

AND FINALLY, FOR A LAUGH,

"I LEARN HOW TO SKATEBOARD."

SO, KNOWING ME, I--

VERY HARD FOR ME TO LEARN THAT

AT MY AGE.

SO, THIS WOULD BE SOMETHING

THAT'S UNLIKELY

THAT I WOULD LEARN HOW TO DO.

SO, IF YOU KNEW SOMETHING ABOUT

YOUR FRIEND,

MAYBE THEY WOULD SAY,

"YOUR FAVOURITE FOOD IS CHIPS,"

FOR EXAMPLE.

AND YOU WOULD SAY,

"YOU KNOW WHAT? IT CERTAINLY IS.

YOU GOT THOSE ODDS RIGHT ON."

SO, YOU CAN WRITE

DIFFERENT LIFE EVENTS

AND SHARE THEM WITH A PARTNER

OR YOUR PARENTS

AND SEE WHERE THEY FALL

ON THE NUMBER LINE.

FOR YOUR SECOND GAME,

Vanessa puts a sheet of paper on the tabletop display.

She says, I WOULD LOVE FOR YOU TO USE

EITHER PLAYING CARDS,

SPINNERS, OR A DIE,

AND HONESTLY,

ALL CAN BE HOMEMADE

WITHIN A FEW MINUTES.

AND YOU'RE GOING TO STATE

A PROBABILITY TO WIN.

SO, IF I SAID I WANT TO MAKE

A GAME

THAT HAS A ONE-IN-FOUR

PROBABILITY TO WIN,

I WOULD MAKE A SPINNER

WITH FOUR SECTIONS ON IT.

IF I SAID I WANTED TO MAKE

A SPINNER--

OR SORRY, A GAME WITH A SPINNER

THAT HAS A PROBABILITY OF ONE

OUT OF SIX AFTER EVERY SPIN,

WE COULD MAKE A SPINNER

LIKE THIS ONE HERE

THAT HAS SIX SECTIONS.

OKAY? SO, IT'S UP TO YOU.

YOU CAN CHOOSE EITHER A SPINNER,

PLAYING CARDS, A DICE, COINS.

WHAT KIND OF GAME

WOULD YOU LIKE TO CREATE?

SO, FOR MY DICE GAME

THAT WE'RE GOING TO PLAY

A LITTLE BIT LATER,

IT'S CALLED MULTIPLY TO WIN.

I'M GOING TO ROLL MY TWO DICE,

AND THE ONLY WAY I CAN WIN

IS IF I ROLL TWO--

THE PRODUCT OF THE TWO ROLLS

HAS TO BE 36.

WHAT DOES THAT MEAN?

HOW CAN I GET 36

WHEN I MULTIPLY

MY TWO ROLLS TOGETHER?

IT MEANS THAT I'D HAVE TO HAVE

MY FIRST DICE, ROLL A SIX,

AND MY SECOND DICE,

ALSO ROLL A SIX.

Two brown dice sit on the table in front of Vanessa.

She says, BECAUSE SIX TIMES SIX

GIVES ME A PRODUCT OF 36.

WHAT ARE THE ODDS OF GETTING 36

AS MY PRODUCT?

WELL, I KNOW I HAVE

A ONE-OUT-OF-SIX CHANCE

OF ROLLING A SIX ON A DICE,

ON A SIX-SIDED DICE.

I ALSO AGAIN HAVE

A ONE-OUT-OF-SIX PROBABILITY

OF ROLLING A SIX

ON MY SECOND ROLL,

BECAUSE IT'S A SIX-SIDED DICE

DOWN HERE

AND THE NUMBER SIX

ONLY OCCURS ONE TIME.

WHEN I MULTIPLY

THOSE TWO NUMBERS TOGETHER,

ONE TIMES ONE IS ONE.

I MULTIPLY MY DENOMINATORS

TOGETHER.

SIX TIMES SIX IS 36.

SO, MY PROBABILITY

OF WINNING MY GAME

IS ONE OUT OF 36.

NOW, IF AGAIN, WE'RE USING IT

ON A NUMBER LINE,

I CAN SEE THAT

IT'S QUITE UNLIKELY

THAT I WILL WIN THIS GAME,

BUT WHY NOT HAVE FUN AND TRY?

SO, GO AHEAD

AND MAKE YOUR OWN GAME,

WHATEVER YOU CHOOSE,

WHATEVER YOU'D LIKE YOUR

PROBABILITY TO BE.

AND PLAY IT WITH A FRIEND,

A SIBLING, A PARENT, A GUARDIAN,

AND LET ME KNOW

HOW MUCH FUN YOU'RE HAVING.

The animated sun rises.

Vanessa continues, HOW ARE THE GAMES GOING?

ARE YOU HAVING A LOT OF FUN?

LET'S TRY MINE.

SO, WE HAD TALKED ABOUT

THEORETICAL PROBABILITY

BEING THE NUMBER OF FAVOURABLE

OUTCOMES

OVER THE NUMBER

OF POSSIBLE OUTCOMES.

AND WE KNOW IN MY GAME,

I REQUIRE BOTH NUMBERS

TO BE SIX,

SO THAT THEY MULTIPLY TO

A PRODUCT OF 36.

SO, I HAVE A ONE-IN-36

PROBABILITY

OF ME WINNING MY GAME.

SO, IT'S NOT VERY LIKELY,

BUT WHY NOT HAVE

A LOT OF FUN DOING IT?

SO, I'M GOING TO ROLL

MY FIRST DICE.

LET'S SEE WHAT I GET

AS MY FIRST.

Vanessa rolls a die and says, I GET A FIVE.

SO, UNFORTUNATELY,

I KNOW THAT NO MULTIPLICATION,

NO PRODUCT WITH A FIVE,

WILL EQUAL 36.

SO, I DIDN'T WIN

THAT FIRST TIME.

LET'S TRY IT AGAIN.

Vanessa rolls the die and says,

I GOT A FOUR.

SO AGAIN, UNFORTUNATELY,

I DIDN'T WIN.

BUT THE PROBABILITY TOLD ME

THAT IT'S VERY UNLIKELY

THAT I WOULD WIN.

OKAY? SO, I CAN MAKE A DECISION

BASED ON HOW LIKELY THE OUTCOME

IS TO HAPPEN GOING FORWARD.

SO, MAYBE AGAIN,

IF I WANTED TO REALLY BEAT

MY FRIENDS,

I COULD SAY, "YOU KNOW WHAT?

IF YOU ROLL TWO SIXES,

YOU CAN WIN," 'CAUSE I KNOW THAT

IT'S VERY, VERY DIFFICULT

FOR THEM TO WIN,

TO ROLL TWO SIXES.

SO, YOU CAN HAVE A LOT OF FUN

WITH YOUR FRIENDS THAT WAY, TOO.

AGAIN, WE'RE GOING TO USE

PROBABILITY IN OUR LIVES

TO MAKE DECISIONS

AND PREDICTIONS.

IF WE KNOW THAT THERE'S

A 10% CHANCE OF RAIN,

WE KNOW THAT IT'S VERY UNLIKELY

THAT YOU HAVE TO BRING

THAT UMBRELLA TO SCHOOL

THAT DAY.

COMPARED TO A 90% CHANCE

OF RAIN,

WHERE IT'S ALMOST CERTAIN

TO RAIN,

YOU'RE GOING TO NEED TO MAKE

A CHANGE OF PLAN

AND PACK THAT UMBRELLA

INTO THAT BACKPACK

BEFORE YOU GET IT--

AS YOU GO OFF TO SCHOOL.

Vanessa holds up the number line.

She says, USING THAT NUMBER LINE,

PLOTTING FROM IMPOSSIBLE

OR NEVER

ALL THE WAY TO CERTAIN, OKAY,

THIS IS GOING TO HELP YOU

UNDERSTAND

HOW LIKELY AN EVENT WILL OCCUR.

IN TERMS OF GAMES,

IN TERMS OF YOUR FAVOURITE TEAM

WINNING THE STANLEY CUP,

THEY'RE ALL EQUALLY AS LIKELY

TO WIN

AT THE BEGINNING OF THE SEASON.

The caption appears that reads, Junior 4-6. Teacher Vanessa.

Vanessa says, I HOPE YOU HAD A LOT OF FUN

WITH TODAY'S EPISODE.

I KNOW I DID. KEEP PRACTISING

THOSE POSITIVE AFFIRMATIONS.

KEEP PRACTISING

USING PHYSICAL ACTIVITY

AS A WARMUP TO GET YOU READY

FOR LEARNING AND EXPLORING,

AND I'LL CATCH YOU NEXT TIME

ON ANOTHER EPISODE

OF

TVOKIDS POWER HOUR

OF LEARNING.

(soft upbeat music plays)

Text reads, TVO kids would like to thank all the teachers involved in the Power Hour of learning as they continue to teach children of Ontario from their homes.

TVO Kids Power Hour of Learning. TVO. Copyright, The Ontario Educational Communications Authority 2021

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