The number of requests for assistance received by a towing service is a poisson process with rate α = 2 per hour. After realizing that he did not miss any calls for assistance when taking a 15 minute...

 The number of requests for assistance received by a towing service is a poisson process with rate α = 2 per hour. After realizing that he did not miss any calls for assistance when taking a 15 minute break, the operator decides to take another 15-minute break. What is the probability that he will not miss any calls again?

We 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.