Answer: $\quad 25$ 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 $12: 14(: 00)$.
1. 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 $12: 14$ ?