Question 139000
The fast train arrives every 15 minutes and waits 4 minutes.  That means that the fast train is there 4 out of every 15 minutes.  Pick a random minute out of any 15, and you have 4 possibilities out of 15 that the fast train will be there; probability {{{4/15}}}


For the second part of the problem.  The fast train is at the station for a total of 4 minutes out of 15, and the local is there 3 minutes out of 15.  Since there is no overlap, the total time that any train is there is 7 minutes.  That means out of every 15 minutes, there are 8 minutes when there is no train there at all.  Hence, the probability of having to wait to get on a train is {{{8/15}}}