HMMT 十一月 2016 · GEN 赛 · 第 2 题
HMMT November 2016 — GEN Round — Problem 2
题目详情
英文原题
- I have five different pairs of socks. Every day for five days, I pick two socks at random withoutreplacement to wear for the day. Find the probability that I wear matching socks on both the thirdday and the fifth day.
解析
英文解析
- I have five different pairs of socks. Every day for five days, I pick two socks at random withoutreplacement to wear for the day. Find the probability that I wear matching socks on both the thirdday and the fifth day.
Proposed by: Kevin Yang
Answer:1
1 163
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 amatching pair on the fifth day with probability . We multiply these probabilities to get .11
637