Question 1108717: Goliath and David play a game in which there are no ties. Each player is equally likely to win each game. The first player to win 4 games becomes the champions and no further games are played. Goliath wins the first 2 games. What is the probability that David becomes the champion ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! since Goliath has won the first two games, David could win the next 4 games or loose one more game - 6 or 7 games to be played
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the probability for each player to win a game is 1/2
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let L be a loss for David and W be a win for David
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we have the following
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(L,L,W,W,W,W), (L,L,L,W,W,W,W), (L,L,W,L,W,W,W), (L,L,W,W,L,W,W), (L,L,W,W,W,L,W)
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(1/2)^6 + 4 * (1/2)^7 = 0.0469
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P ( David is the Champion ) = 0.0469
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