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HMMT 二月 2009 · GEN1 赛 · 第 5 题

HMMT February 2009 — GEN1 Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
解析
  1. [ 4 ] Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers? Answer: 52 / 3 1 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.