HMMT 二月 2002 · 代数 · 第 4 题
HMMT February 2002 — Algebra — Problem 4
题目详情
- If a positive integer multiple of 864 is picked randomly, with each multiple having the same probability of being picked, what is the probability that it is divisible by 1944? 2 3
解析
- If a positive integer multiple of 864 is picked randomly, with each multiple having the same probability of being picked, what is the probability that it is divisible by 1944? 5 3 3 5 Solution: The probability that a multiple of 864 = 2 3 is divisible by 2744 = 2 3 is 2 2 the same as the probability that a multiple of 2 is divisible by 3 , which since 4 and 9 are 1 relatively prime is . 9 2 3