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HMMT 二月 2009 · COMB 赛 · 第 2 题

HMMT February 2009 — COMB Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. Whatis the expected number of cards that will be strictly between the two jokers?
解析

英文解析

  1. [ 3 ] Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. Whatis the expected number of cards that will be between the two jokers?
    Answer: 52 / 3
    Solution: Each card has an equal likelihood of being either on top of the jokers, in between them,
    or below the jokers. Thus, on average, 1 / 3 of them will land between the two jokers.