HMMT 十一月 2016 · GEN 赛 · 第 2 题
HMMT November 2016 — GEN Round — Problem 2
题目详情
- I have five different pairs of socks. Every day for five days, I pick two socks at random without replacement to wear for the day. Find the probability that I wear matching socks on both the third day and the fifth day.
解析
- I have five different pairs of socks. Every day for five days, I pick two socks at random without replacement to wear for the day. Find the probability that I wear matching socks on both the third day and the fifth day. Proposed by: Kevin Yang 1 Answer: 63 1 1 I get a matching pair on the third day with probability because there is a probability of the 9 9 second sock matching the first. Given that I already removed a matching pair of the third day, I get a 1 1 matching pair on the fifth day with probability . We multiply these probabilities to get . 7 63