HMMT 十一月 2008 · 冲刺赛 · 第 22 题
HMMT November 2008 — Guts Round — Problem 22
题目详情
英文原题
- [ 12 ] Sandra the Maverick has 5 pairs of shoes in a drawer, each pair a different color. Every day for
5 days, Sandra takes two shoes out and throws them out the window. If they are the same color, shetreats herself to a practice problem from a past HMMT. What is the expected value (average number)
of practice problems she gets to do?
2 2 2
( x − 4) y y 2 x
解析
英文解析
- [ 12 ] Sandra the Maverick has 5 pairs of shoes in a drawer, each pair a different color. Every day for
5 days, Sandra takes two shoes out and throws them out the window. If they are the same color, shetreats herself to a practice problem from a past HMMT. What is the expected value (average number)
of practice problems she gets to do?
5 1
Answer: On any given day, there is a chance that the second shoe that Sandra chooses makes
9 9
a pair with the first shoe she chose. Thus the average number of problems she does in a day is , so,1
by the linearity of expectation, she does problems total, on average.59
2 229
( x − 4)2
y yx