SOLUTION: the probability that a man wins a game is 3/4 . he plays the game until he wins. determine the probability that he wins in the fifth round.

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Question 1101533: the probability that a man wins a game is 3/4 . he plays the game until he wins. determine the probability that he wins in the fifth round.
Answer by Theo(13342) About Me  (Show Source):
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if he registers his first win in the fifth round, that means he lost in rounds 1 through 4.

the probability that he wins a game is 3/4.
the probability that he loses a game is therefore 1 - 3/4 = 1/4

the probability that he loses in the first four round and then wins in the fifth round is therefore:

1/4 * 1/4 * 1/4 * 1/4 * 3/4.