Question

Suppose that two teams (for fun, let’s call them the Domestic Shorthairs and Cache Cows) play a
series of games to determine a winner. In a best-of-three series, the games end as soon as one
team has won two games. In a best-of-five series, the games end as soon as one team has won
three games, and so on. Assume that the Domestic Shorthair’s probability of winning any one
game is p, where .5 < p < 1. (Notice that this means that the Domestic Shorthairs are the better
team.) Also assume that the outcomes are independent from game to game.
We will compare different series configurations/rules on two criteria: the probability that the
better team wins the series, and the expected value of the number of games needed to complete
the series.
Best-of-Three Series
a) Determine (exactly) the probability that the Domestic Shorthairs win a best-of-three series, as
a function of p. (Show your work. Also note that you solved this for a particular value of p in
Quiz 4, so you might want to review that quiz.)

Answer 1

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