HMMT 二月 2001 · GEN2 赛 · 第 6 题

HMMT February 2001 — GEN2 Round — Problem 6

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

解析

You take a wrong turn on the way to MIT and end up in Transylvania, where 99% of the inhabitants are vampires and the rest are regular humans. For obvious reasons, you want to be able to figure out who’s who. On average, nine-tenths of the vampires are correctly identified as vampires and nine-tenths of humans are correct identified as humans. What is the 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. So 1 out of the 108 who pass, only are human. 12 [ ] 1 1