HMMT 二月 2001 · 冲刺赛 · 第 17 题

HMMT February 2001 — Guts Round — Problem 17

[4] Frank and Joe are playing ping pong. For each game, there is a 30% chance that Frank wins and a 70% chance Joe wins. During a match, they play games until someone wins a total of 21 games. What is the expected value of number of games played per match? 10 8 6 4 2

解析

[4] Frank and Joe are playing ping pong. For each game, there is a 30% chance that Frank wins and a 70% chance Joe wins. During a match, they play games until someone wins a total of 21 games. What is the expected value of number of games played per match? Solution: The expected value of the ratio of Frank’s to Joe’s score is 3:7, so Frank is expected to win 9 games for each of Frank’s 21. Thus the expected number of games in a match is 30 . 10 8 6 4 2