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HMMT 二月 2001 · GEN2 赛 · 第 6 题

HMMT February 2001 — GEN2 Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. You take a wrong turn on the way to MIT and end up in Transylvania, where 99% ofthe inhabitants are vampires and the rest are regular humans. For obvious reasons, you wantto be able to figure out who’s who. On average, nine-tenths of the vampires are correctlyidentified as vampires and nine-tenths of humans are correct identified as humans. What isthe probability that someone identified as a human is actually a human?
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解析

英文解析

  1. You take a wrong turn on the way to MIT and end up in Transylvania, where 99% ofthe inhabitants are vampires and the rest are regular humans. For obvious reasons, you wantto be able to figure out who’s who. On average, nine-tenths of the vampires are correctlyidentified as vampires and nine-tenths of humans are correct identified as humans. What isthe probability that someone identified as a human is actually a human?
    Solution: Consider a sample of 1000 inhabitants. On average, 990 are vampires and 10
    are people. 99 vampires are identified as human and 9 humans are identified as human. Soout of the 108 who pass, only are human.1
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    1 1