HMMT 二月 2005 · COMB 赛 · 第 3 题

英文解析

3. The Red Sox play the Yankees in a best-of-seven series that ends as soon as one teamn − 1
   wins four games. Suppose that the probability that the Red Sox win Game n is .
   What is the probability that the Red Sox will win the series?6
   Solution: 1 / 2
   Note that if we imagine that the series always continues to seven games even after oneteam has won four, this will never change the winner of the series. Notice also that the probability that the Red Sox will win Game n is precisely the probability that the
   Yankees will win Game 8 − n . Therefore, the probability that the Yankees win at leastfour games is the same as the probability that the Red Sox win at least four games,
   namely 1 / 2.