HMMT 二月 2015 · COMB 赛 · 第 1 题
HMMT February 2015 — COMB Round — Problem 1
题目详情
- Evan’s analog clock displays the time 12:13; the number of seconds is not shown. After 10 seconds elapse, it is still 12:13. What is the expected number of seconds until 12:14?
解析
- Evan’s analog clock displays the time 12:13; the number of seconds is not shown. After 10 seconds elapse, it is still 12:13. What is the expected number of seconds until 12:14? Answer: 25 At first, the time is uniformly distributed between 12:13:00 and 12:13:50. After 10 seconds, the time is uniformly distributed between 12:13:10 and 12:14:00. Thus, it takes on average 25 seconds to reach 12:14(:00).