PROBABILITY AND EXPECTED VALUE THE GAME OF PIG PROBABILITY AND EXPECTED VALUE

THE GAME OF PIG IF YOU ROLL A 1, THEN YOUR TURN IS OVER ROLL A SIX SIDED DIE

WRITE DOWN THE BEST STRATEGY PIG STRATEGIES WRITE DOWN THE BEST STRATEGY

A DOUBLE MEANS HAVING THE SAME NUMBER SHOW ON BOTH DICE WAITING FOR A DOUBLE A DOUBLE MEANS HAVING THE SAME NUMBER SHOW ON BOTH DICE

GAMBLERS FALLACY WE WILL CALL THREE IDENTICAL FLIPS IN A ROW A TRIPLET

VOCABULARY THEORETICAL PROBABILITY OBSERVED PROBABILITY IS PROBABILITY DETERMINED ON THE BASIS OF A MODEL OBSERVED PROBABILITY IS PROBABILITY BASED ON ACTUAL RESULTS OF PAST EVENTS

WHAT ARE THE CHANCES? THEORETICAL OR OBSERVED

PAULA’S PIZZA HOW MANY DIFFERENT POSSIBILITIES?

RUG GAMES DO WE HAVE EQUAL REGIONS?

THE COUNTER’S GAME PLACE 11 MARKERS ROLL A PAIR OF DICE

ROLLIN’ ROLLIN’ ROLL A PAIR OF DICE 50 TIMES

THE THEORY OF TWO-DICE SUMS DEVELOP A RUG DIAGRAM

TWO-DICE SUMS AND PRODUCTS DEVELOP ANOTHER RUG DIAGRAM

SPINNER GIVE AND TAKE MAKE A SPINNER AND PLAY THE GAME

MIA’S CARDS HEARTS WORTH 10 PTS A STANDARD DECK OF CARDS CLUB, SPADE, DIAMONDS WORTH 5 PTS A STANDARD DECK OF CARDS

EXPECTED VALUE IS THE AVERAGE AMOUNT GAINED (OR LOST) PER TURN IN THE LONG RUN

A FAIR RUG GAME? CRYSTAL WINS $5 TONY WINS $3

ONE-AND-ONE 60% CHANCE OF MAKING THE FREE THROW

A SIXTY-PERCENT SOLUTION SIMULATION 40 TIMES

THE THEORY OF ONE-AND-ONE DEVELOP A RUG DIAGRAM AND FIND THE EXPECTED VALUE

STREAK-SHOOTING SHELLY EXPECTED VALUE

SPINS AND DRAWS CHARITY ARCIBALD BEATRICE

MARTIAN BASKETBALL 1ST SHOT 60% 80% 2ND AND 90% 3RD

THE CARRIER’S PAYMENT PLAN QUANDARY $5 OR PICK TWO BILLS AND RECEIVE $11 OR $2

THE GAME OF LITTLE PIG RED CUBE = 1 POINT BLUE CUBE = 4 POINTS YELLOW CUBE = 0 POINTS

LITTLE PIG STRATEGIES THE TWO POINT STRATEGY THE TWO DRAW STRATEGY

LITTLE PIG STRATEGIES THE THREE POINT STRATEGY THE THREE DRAW STRATEGY

LITTLE PIG STRATEGIES THE FOUR POINT STRATEGY THE FOUR DRAW STRATEGY

LITTLE PIG STRATEGIES THE FIVE POINT STRATEGY THE FIVE DRAW STRATEGY

LITTLE PIG STRATEGIES THE SIX POINT STRATEGY THE SIX DRAW STRATEGY

SHOULD I GO ON? WHICH STRATEGY IS BETTER? POINT OR DRAW??????

THE BEST LITTLE PIG FOR WHAT SCORES DOES IT PAY TO DRAW AGAIN? FOR WHAT SCORES DOES IT PAY TO STOP?

BIG PIG MEETS LITTLE PIG AFTER HOW MANY POINTS SHOULD WE STOP ROLLING THE DIE?

SOLVING THE UNIT PROBLEM SUMMARIZE WHAT YOU HAVE LEARNED ABOUT THE BEST POSSIBLE STRATEGY FOR PIG.

WAITING FOR A DOUBLE MAKE A PREDICTION DO THE EXPERIMENT 10 TIMES WHAT WAS THE LARGEST # OF ROLLS TO GET A DOUBLE? WHAT WAS THE AVG OF THE TEN EXPERIMENTS?

WAITING FOR A DOUBLE HOW CLOSE IS YOUR PREDICTED AVERAGE TO THE YOUR EXPERIMENTS AVERAGE?

WAITING FOR A DOUBLE MAKE A FREQUENCY BAR GRAPH OF THE CLASSES DATA

THE GAMBLER’S FALLACY WHAT DO YOU THINK ABOUT THE STRATEGY THE PEOPLE USED IN 1913 AT THE CASINO IN MONTE CARLO?

THE GAMBLER’S FALLACY FLIP A COIN 25 TIMES AND RECORD EACH FLIP FIND HOW MANY “SAME’S” AND “DIFFERENT’S” YOU GET

THE GAMBLER’S FALLACY WHAT DOES THE GAMBLERS FALLACY SAY ABOUT THE ROULETTE STRATEGY? HOW IS THE GAMBLER’S FALLACY RELATED TO STRATEGIES FOR THE GAME OF PIG...

THE GAMBLER’S FALLACY …DID YOU SOMETIMES STOP ROLLING BECAUSE YOU THOUGHT THERE WAS NOW A GREATER CHANCE OF ROLLING A 1?

WHAT ARE THE CHANCES? REACHING INTO A BAG WITH 3 RED, 2 BLUE, AND 4 BLACK GUM BALLS AND PULLING OUT A BLUE? FLIPPING A COIN TWICE AND GETTING DIFFERENT RESULTS?

WHAT ARE THE CHANCES? SNOW FALLING SOMETIME IN JULY IN FLORIDA SNOW FALLING SOMETIME IN JULY IN NEW ZEALAND

WHAT ARE THE CHANCES? GOING TO A STORE AND NOT FINDING A T-SHIRT IN YOUR SIZE. A STUDENT IN YOUR MATH CLASS WEARING SNEAKERS.

WHAT ARE THE CHANCES? ROLLING A DIE AND GETTING A PRIME NUMBER. ROLLING 2 DICE AND GETTING DOUBLES. ROLLING A PAIR OF DICE AND GETTING DOULBES BY THE 3RD ROLL.

PAULA’S PIZZA WHAT IS THE PROBABILITY SHE WILL GET WHAT SHE ORDERED? WHAT IS THE PROBABILITY SHE WILL NOT?

PAULA’S PIZZA PAULA ACTUALLY LIKES SAUSAGE AND PEPPERONI TOO. WHAT IS THE PROBABILITY SHE WILL GET A PIZZA SHE LIKES? AND THE PROBABILITY SHE DOESN’T?

RUG GAMES WHAT’S THE PROBABILITY OF BEING HIT FOR EACH COLOR?

RUG GAMES

RUG GAMES

ROLLIN’, ROLLIN’, ROLLIN’ ROLL A PAIR OF DICE 50 TIMES AND RECORD THE SUMS DRAW A GRAPH OF THE DATA YOU GATHERED

ROLLIN’, ROLLIN’, ROLLIN’ WHAT NEW THOUGHTS DOES THIS EXPERIMENT GIVE YOU ABOUT HOW TO PLAY THE COUNTERS GAME?

THEORY OF TWO DICE SUMS

TWO-DICE SUMS AND PRODUCTS WHICH IS MORE LIKELY--THAT THE SUM IS AN ODD NUMBER OR THAT THE SUM IS AN EVEN NUMBER? MAKE UP TWO PROBABILITY QUESTIONS ABOUT 2 DICE SUMS.

TWO-DICE SUMS AND PRODUCTS WHAT ARE THE POSSIBLE TWO-DICE PRODUCTS? WHAT IS THE PROBABILITY OF GETTING EACH OF THE TWO-DICE PRODUCTS?

TWO-DICE SUMS AND PRODUCTS

TWO-DICE SUMS AND PRODUCTS WHICH IS MORE LIKELY--THAT THE TWO-DICE PRODUCT IS AN ODD NUMBER OR THAT THE TWO-DICE PRODUCT IS AN EVEN NUMBER?

SPINNER GIVE AND TAKE WRITE DOWN WHO YOU PREDICT TO BE THE WINNER OF THIS GAME. NOW PLAY THE GAME 25 TIMES AND RECORD YOUR RESULTS.

SPINNER GIVE AND TAKE IF AL AND BETTY PLAY 100 GAMES, HOW FAR AHEAD IS THE EXPECTED WINNER LIKELY TO BE?

MIA’S CARDS IF MIA PICKS A CARD MANY TIMES, WHAT WILL BE HER AVERAGE NUMBER OF POINTS FOR EACH TIME SHE PICKS A CARD?

MIA’S CARDS ON FEB. 14TH, SHE CHANGES THE GAME. 20 PTS FOR A HEART 15 PTS FOR A DIAMOND 0 PTS FOR A CLUB OR SPADE WHAT WOULD HER AVERAGE SCORE PER CARD BE?

A FAIR RUG GAME? IS THIS A FAIR GAME? WHAT IS TONY’S EXPECTED VALUE FOR EACH TURN? WHAT IS CRYSTAL’S?

A FAIR RUG GAME? IF YOU THINK THE GAME IS NOT FAIR, CHANGE THE AMOUNT OF MONEY THEY EACH WIN IN ORDER TO MAKE IT A FAIR GAME.

A SIXTY-PERCENT SOLUTION DO THE SIMULATION 40 TIMES WHAT WAS THE MOST FREQUENT OUTCOME? WHAT WAS THE AVERAGE SCORE?

THE THEORY OF ONE-AND-ONE

STREAK-SHOOTING SHELLY IN WHAT % OF SITUATIONS WILL SHELLY SCORE NO POINTS? ONE POINT? TWO POINTS?

STREAK-SHOOTING SHELLY WHAT IS SHELLY’S EXPECTED VALUE PER ONE-AND-ONE SITUTAION?

SPINS AND DRAWS AL’S WINS 1/5 OF THE TIME BETTY’S WINS 4/5 OF THE TIME AL WINS $1.25 BETTY WINS 30 CENTS

SPINS AND DRAWS WHAT IS AL’S EXPECTED VALUE PER SPIN? WHAT IS BETTY’S EXPECTED VALUE PER SPIN?

SPINS AND DRAWS HOW MIGHT THE PAYMENTS BE CHANGED SO THAT THE GAME IS FAIR?

SPINS AND DRAWS ARCHIBALD CHARITY WINS A PENNY IF WINS 20 CENTS IF NEITHER A JACK OR HEART IS DRAWN ARCHIBALD WINS 20 CENTS IF A JACK IS DRAWN BEATRICE WINS 8 CENTS IF A HEART IS DRAWN

MARTIAN BASKETBALL HOW MANY POINTS IS SHE MOST LIKELY TO SCORE IN A ONE-AND-ONE SITUATION? 1ST SHOT 60 % 2ND SHOT 80% 3RD SHOT 90%

THE CARRIER’S PAYMENT PLAN QUANDARY

THE CARRIER’S PAYMENT PLAN QUANDARY

TWO POINT STRATEGY

TWO DRAW STRATEGY

THREE POINT STRATEGY

THREE DRAW STRATEGY

LITTLE PIG POINTS VS DRAWS

LITTLE PIG POINTS VS DRAWS

THE BEST LITTLE PIG BASED ON YOUR FINDINGS, WHAT STRATEGY WILL GIVE THE HIGHEST POSSIBLE EXPECTED VALUE PER TURN?