HMMT 二月 2013 · COMB 赛 · 第 2 题
HMMT February 2013 — COMB Round — Problem 2
题目详情
英文原题
If Alex does not sing on Saturday, then she has a 70% chance of singing on Sunday; however , to rest
her voice, she never sings on both days. If Alex has a 50% chance of singing on Sunday, find t he
probability that she sings on Saturday.
解析
英文解析
- If Alex does not sing on Saturday, then she has a 70% chance of singing on Sunday; however, to resther voice, she never sings on both days. If Alex has a 50% chance of singing on Sunday, find the probability that she sings on Saturday.
Answer: Let p be the probability that Alex sings on Saturday. Then, the probability that she 2
sings on Sunday is . 7(1 − p ); setting this equal to . 5 gives p = .27 7