Cars arrive at a petrol station at an average rate of 30 per hour. Assuming that the cars arrive at random, find the probability that

(a) no cars arrive during a particular five-minute interval,

(b) more than three cars arrive during a five-minute interval,

(c) more than five cars arrive in a 15-minute interval,

(d) in a half hour period, ten cars arrive,

(e) fewer than three cars arrive in a ten-minute interval.