Question

Trains headed for destination A arrive at the train station at 15-minute intervals starting at 7 A.M., whereas trains headed for destination B arrive at 15-minute intervals starting at 7:05 A.M. (a) If a certain passenger arrives at the station at a time uniformly distributed between 7 and 8 A.M. and then gets on the first train that arrives, what proportion of time does he or she go to destination A

Answer 1

2/3

Explanation:

In the 5-minute interval between 7:00 and 7:05, a train to B is the first to arrive. In the 10-minute interval between 7:05 and 7:15, a train to A is the first to arrive. That is, in any 15-minute interval, the probability is 10/15 = 2/3 that a train to A is the first to arrive.

The 1-hour interval between 7 A.M. and 8 A.M. is an integer number of such intervals, so ...

2/3 of the time, he or she will go to destination A.