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Oh Craps! AMATYC Presentation November 2009 Lance Phillips – Tulsa Community College The Vocabulary of Probability • Experiment – A situation which involves chance or probability the result of which is called an outcome. • Outcome – The result of a single trial of an experiment. • Event – One or more outcomes of an experiment. • Probability – The measure of how likely an event is. Setting up a Simple Experiment – The Coin Toss • Call it! > Heads > Tails P(event) = number of favorable outcomes ______ total number of equally likely outcomes Coin Toss Outcome • Heads – One (1) possibility • Tails – One (1) possibility Using a Tree Diagram to Illustrate Outcomes H P(H) = 1/2 T P(T) = 1/2 Coin Toss Tally Sheet Study 1 Heads _________ Tails ________ Total _____ Study 2 _________ ________ _____ Study 3 Total _________ ____ ________ ____ _____ ____ Observed Ratio __/__ __ / __ Advancing the Experiment • Two tosses of the coin 1st Toss 2nd Toss H Outcomes H,H H T H H,T T,H T T T,T Probability of tossing two tails is 1 in 4. What then is the probability of a tail and a head, in no specific order? ______ Advancing the Experiment • Three tosses of the coin 1st Toss 2nd Toss 3rd Toss Outcomes H H,H,H T H,H,T H H,T,H T H,T,T 8 possible H T,H,H outcomes T T,H,T H T ,T,H T T,T,T H H T H T T Probability of tossing three tails is 1 in 8. Advancing the Experiment Four tosses of a single coin • • • • • • • • HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT • • • • • • • • THHH THHT THTH THTT TTHH TTHT TTTH TTTT Playing Cards • How many cards in a deck? • Probability of drawing the ace of hearts? • Probability of drawing an ace? • Probability of drawing a heart? Rolling a Die • Possible outcomes: – 1, 2, 3, 4, 5, 6 > Probability of rolling a 4 is 1 in 6 > Probability of rolling a 2 is 1 in 6 > Probability of rolling an even number 3 in 6 which we simplify to 1 in 2 Rolling a Pair of Dice • 36 Different possible outcomes 2 3 4 5 6 7 8 9 10 11 12 Percentage of Dice Totals Appearing Dice Total 2, 12 3, 11 4, 10 5, 9 6, 8 7 Likelihood 1/36 = 2.78% 2/36 = 5.56% 3/36 = 8.33% 4/36 = 11.11% 5/36 = 13.89% 6/36 = 16.67% Probability Versus Odds • Probability : Favorable outcomes to possible outcomes – probability of rolling a nine is 4 in 36 or 1 in 9. • Odds: Wrong outcomes to right outcomes (or opposite) – Odds of rolling a nine are 8 to 1 against. • What is the probability of rolling a four? • What are the odds of rolling a four? Combinations leading to 7 Basic Craps The Playing Field A Typical Commercial Craps Table Basic Craps Vocabulary: Shooter Come Out Roll – The Point A Natural Craps – Come Don’t Come The Field - Regular Craps Rules • Game begins by “Stickman” passing dice to next player in clockwise rotation. • First roll 7 or 11 Wins P=2/9 • First roll 2, 3, or 12 Loses P=1/9 • On first roll a roll of 4, 5, 6, 8, 9, or 10 establishes the “point” number. • Win on subsequent rolls if “point” appears before a 7. Pass Line Bets Don’t Pass Bet The Come Bet The Don’t Come Bet Field Bets Place Bets Resources • Felts available on Ebay or Amazon ranging in price from $5 - $40, • Foldable table tops from $45 - $150. • Pucks around $10. • Dice anywhere. • Lance Phillips – [email protected]