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HMMT 十一月 2016 · 冲刺赛 · 第 1 题

HMMT November 2016 — Guts Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] If five fair coins are flipped simultaneously, what is the probability that at least three of them showheads?
    10
解析

英文解析

  1. [ 5 ] If five fair coins are flipped simultaneously, what is the probability that at least three of them showheads?
    Proposed by: Allen Liu
    Answer:1
    The coin either lands heads-up at least three times or lands heads-down at least three times. These 2
    scenarios are symmetric so the probably is just .1
    5 5 52 + +
    ( ) ( ) ( )
    3 4 5 16 1
    Alternatively, we can explicitly compute the probability, which is just = =
    2 32 25
    10