The question is as follows:
A short film will show three times tomorrow - at $12:00, 13:30$ and $15:00$. If you arrive at the theatre at a random time between $12:30$ and $14:30$, what is the probability that you will have to wait less than 30 minutes for the next show to start?
So far I've managed this:
I modeled $t$ in hours thereby making the PDF = $f_X(x) = 1/(b-a) = 1/(3-0) = 1/3$
I attempted to find the probability of 30 minutes before each show that I had not missed which in this case would be the $13:30$ and $15:00$ shows giving the equation: $Pr( 13:00 < t < 13:30) + Pr(14:30) = (0.5)*(1/3) + 0 = 0.166... = 0.17$
But I don't think this is all to the answer and I can't figure out what else to do.