The number of cars approaching a toll booth in a minute follows a geometric random variable with a mean of 2 cars/minute. The time it takes the toll collector to serve each car is an exponential random variable with a mean of 20 seconds.

(a) Find the mean time that the toll collector will require to serve cars that arrive in a one-minute interval.

(b) Find the PDF of the time that the toll collector will require to serve cars that arrive in a one-minute interval.

(c) What is the probability that the toll collector will require more than one minute to serve the cars that arrive during a one-minute interval, thereby causing a queue to form?