Question 124
Every day at a railway station, there is just one train arriving between $8{:}00$ am and $9{:}00$ am and between $9{:}00$ am and $10{:}00$ am, respectively. The arrival times and their probabilities for the two trains are shown in the following table:
| Train A arrival time | $8{:}10$ | $8{:}30$ | $8{:}50$ |
|---|---|---|---|
| Train B arrival time | $9{:}10$ | $9{:}30$ | $9{:}50$ |
| Probability | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{1}{3}$ |
Suppose that these random events are independent of each other. Now, a traveler comes into the station at $8{:}20$. Then the mathematical expectation of his waiting time is ______ (round to minute).
| Train A arrival time | $8{:}10$ | $8{:}30$ | $8{:}50$ |
|---|---|---|---|
| Train B arrival time | $9{:}10$ | $9{:}30$ | $9{:}50$ |
| Probability | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{1}{3}$ |
Suppose that these random events are independent of each other. Now, a traveler comes into the station at $8{:}20$. Then the mathematical expectation of his waiting time is ______ (round to minute).