HMMT 十一月 2009 · GEN2 赛 · 第 7 题

HMMT November 2009 — GEN2 Round — Problem 7

[ 4 ] Five guys are eating hamburgers. Each one puts a top half and a bottom half of a hamburger bun on the grill. When the buns are toasted, each guy randomly takes two pieces of bread off of the grill. What is the probability that each guy gets a top half and a bottom half? Page 1 of 2

解析

[ 4 ] Five guys are eating hamburgers. Each one puts a top half and a bottom half of a hamburger bun on the grill. When the buns are toasted, each guy randomly takes two pieces of bread off of the grill. What is the probability that each guy gets a top half and a bottom half? 8 Answer: Say a guy is content if he gets a top half and a bottom half. Suppose, without loss of 63 5 generality, that the first guy’s first piece of bread is a top. Then there is a chance that his second 9 4 piece of bread is a bottom. By the same reasoning, given that the first guy is content, there is a 7 3 chance that the second guy is content. Given that the first two guys are content, there is a chance 5 5 4 3 2 1 8 that the third guy is content, and so on. Our final answer is · · · · = . 9 7 5 3 1 63