You arrive at a bus stop at 8:00 a.m. knowing that the bus will arrive at some time uniformly distributed between 8:45 and 9:03. (a) What is the probability that you will wait at least 40 minutes? (b) What is the probability that you will wait more than 51 minutes? (c) What is the probability that you will wait at most 57 minutes? (d) What is the probability that you will wait at least 50 minutes? (Hint: what is the relationship between the bus's arrival and your waiting?)