Fahrettin and Recep are enrolled in OR-III course. Group taxis are waiting for passengers at the central railway station. Passengers for those taxis arrive according to a Poisson process with an average of passengers per hour. A taxi departs as soon as four passengers have been collected or minutes have expired since the first passenger got in the taxi.

(a) Suppose you get in the taxi as first passenger. What is the probability that you have to wait minutes until the departure of the taxi?

(b) Suppose you got in the taxi as first passenger and you have already been waiting for /2 minutes. In the meantime two other passengers got in the taxi. What is the probability that you will have to wait another /2 minutes until the taxi departs?