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