HMMT 二月 2015 · COMB 赛 · 第 2 题
HMMT February 2015 — COMB Round — Problem 2
题目详情
英文原题
- Victor has a drawer with 6 socks of 3 different types: 2 complex socks, 2 synthetic socks, and 2
trigonometric socks. He repeatedly draws 2 socks at a time from the drawer at random, and stops ifthe socks are of the same type. However, Victor is “synthetic-complex type-blind”, so he also stops ifhe sees a synthetic and a complex sock.
What is the probability that Victor stops with 2 socks of the same type? Assume Victor returns bothsocks to the drawer after each step.
解析
英文解析
- Victor has a drawer with 6 socks of 3 different types: 2 complex socks, 2 synthetic socks, and 2
trigonometric socks. He repeatedly draws 2 socks at a time from the drawer at random, and stops ifthe socks are of the same type. However, Victor is “synthetic-complex type-blind”, so he also stops ifhe sees a synthetic and a complex sock.
What is the probability that Victor stops with 2 socks of the same type? Assume Victor returns bothsocks to the drawer after each step.
Answer: Let the socks be C , C , S , S , T , T , where C , S and T stand for complex, synthetic 3
1 2 1 2 1 2
and trigonometric respectively. The possible stopping points consist of three pairs of socks of the same 7
type plus four different complex-synthetic ( C - S ) pairs, for a total of 7. So the answer is .3 7