(a)The number of requests for assistance received by a towing service is a poisson process with rate α = 2 per hour. If the operator takes a 15-minute break, what is the probability that he does not...

(a)The number of requests for assistance received by a towing service is a poisson process with rate α = 2 per hour. If the operator takes a 15-minute break, what is the probability that he does not miss any calls for assistance?

(b) After realizing that he did not miss any calls for assistance, the operator decides to take another 15-minute break. What is the probability that he will not miss any calls again?

Hint:
Want to determine
P[no calls in time interval (0 , 1/2)│no calls in time interval (0 , 1/4)],
where the unit used for time interval is hours.

(c)  Automobiles arrive at a vehicle equipment inspection station according to a Process process with rate α = 6 per hour. Suppose that with probability π = 0.4 an arriving vehicle will have no equipment violations. What is the probability that five “no-violation” cars arrive during the next hour?