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HMMT 二月 2004 · COMB 赛 · 第 4 题

HMMT February 2004 — COMB Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row
    (the sequence HH ) or flips tails followed by heads (the sequence T H ). What is the probability that she will stop after flipping HH ?
解析

英文解析

  1. Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row
    (the sequence HH ) or flips tails followed by heads (the sequence T H ). What is the probability that she will stop after flipping HH ?
    Solution: 1 / 4
    The only way that Andrea can ever flip HH is if she never flips T , in which case she 1
    must flip two heads immediately at the beginning. This happens with probability .1 4