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Unformatted text preview: Pi = Example Alice and Bob are playing a game. Each game, the loser pays the winner $5. Bob has $50 and Alice has $25 to start. a) If the game is fair, find the probability that Bob loses b) If the game is biased so that Alice has a 60% chance of winning each game, again find the probability that Bob loses. Solution Let 1 unit be $5. Then Bob has 10 units and Alice has 5. The total bankroll is 15 units so k = 15. a) p = q = 0.5 here. P(Bob loses) = P(Alice wins) = i/k = 5/15 = 0.33 b) p = 0.6, q = 0.4, and P(Bob loses) = P(Alice wins) = [1 (0.4/0.6) 5 ] / [1 (0.4/0.6) 15 ] = 0.87...
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This note was uploaded on 12/12/2010 for the course STAT 4670 taught by Professor Skrzydlo,dianakatherine during the Spring '10 term at Waterloo.
- Spring '10