Two teams are playing a best-of-five series, which ends as soon as either team wins three games. If the two teams are equally likely to win a game, regardless of the outcomes of the others, what is the probability that the series ends after the first three games?
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Correct Answer: C. 1/4
The series will end after the first three games if either of the teams wins all three in a row. The probability that Team-A wins one game is 1/2, and the probability that Team-A wins the first three games is 1/2×1/2×1/2=1/8. Similarly, the probability that Team-B wins the first three games is 1/8. So the probability that either Team-A or Team-B wins the first three games is 1/8+1/8=1/4.
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