Library / /668 of 1394

, 2015

Combinatorics Difficulty 5.2 AIME, harder Prove it United States

Problem:

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 $12:14$ ?

Solution

Solution:

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).

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