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HMMT 二月 2015 · COMB 赛 · 第 1 题

HMMT February 2015 — COMB Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Evan’s analog clock displays the time 12:13; the number of seconds is not shown. After 10 secondselapse, it is still 12:13. What is the expected number of seconds until 12:14?
解析

英文解析

  1. Evan’s analog clock displays the time 12:13; the number of seconds is not shown. After 10 secondselapse, 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).