HMMT 二月 2016 · 冲刺赛 · 第 9 题
HMMT February 2016 — Guts Round — Problem 9
题目详情
英文原题
- [ 7 ] Victor has a drawer with two red socks, two green socks, two blue socks, two magenta socks, twolavender socks, two neon socks, two mauve socks, two wisteria socks, and 2000 copper socks, for a totalof 2016 socks. He repeatedly draws two socks at a time from the drawer at random, and stops if thesocks are of the same color. However, Victor is red-green colorblind, so he also stops if he sees a redand green sock.
What is the probability that Victor stops with two socks of the same color? Assume Victor returnsboth socks to the drawer at each step.
解析
英文解析
- [ 7 ] Victor has a drawer with two red socks, two green socks, two blue socks, two magenta socks, twolavender socks, two neon socks, two mauve socks, two wisteria socks, and 2000 copper socks, for a totalof 2016 socks. He repeatedly draws two socks at a time from the drawer at random, and stops if thesocks are of the same color. However, Victor is red-green colorblind, so he also stops if he sees a redand green sock.
What is the probability that Victor stops with two socks of the same color? Assume Victor returnsboth socks to the drawer at each step.
Proposed by: Evan Chen
1999008
Answer:
1999012
( ) ( )
2000 2
There are + 8 = 1999008 ways to get socks which are matching colors, and four extra
2 2
ways to get a red-green pair, hence the answer.