(a) Two teams, A and B, are playing in the best-of-7 World Series; whoever gets to...

(a) Two teams, A and B, are playing in the best-of-7 World Series; whoever gets to 4 wins first wins the series. Suppose the home team always has a small advantage, winning each game with probability 0.6 and losing with probability 0.4. Also assume that every game is independent. What is the probability that team A will win the series in exactly 6 games if the series is played in the following format: A–A–B–B–B–A–A, meaning that the first two games are played on team A’s field, followed by three games on team B’s field, and the final two games back on team A’s field?

[Note: Do not use the negative binomial straight up. You will run into trouble, because in this case, the winning probability shifts from one team to the other depending on who has the home field advantage.]

(b) You’re a huge Boston Red Sox fan, and in the current1 best-of-7 World Series they have a probability of p = 0.4 of winning each game. After the Sox lose Game 1, you get so inebriated that you sleep for two days, and miss the next two games. Upon awakening, you rush out to the street and ask the first person you see, “What happened in Games 2 and 3?” “They split them,” comes the reply. Should you be happy? In other words, how do the Sox’s chances of winning look now compared to after Game 1?

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orchestra answered 1 year ago

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