Suppose the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. Round the answers to 3 decimal places.
(a) What is the probability that there are no counts in a 30-second interval?
(b) What is the probability that the first count occurs in less than 7 seconds?
(c) What is the probability that the first count occurs between 1 and 2 minutes after start-up?