$5.$ You wait at the post office. There are two queues. In each queue a clerk serves customers, and the service time is exponentially distributed $($and independent for the various customers$).$ The first queue has one customer waiting $($i$.$e$.$ being in service$)$ before you, and the clerk serves customers at rate $1$ per hour. The second has two

customers waiting $($one being in service, and a second not waiting for the first to finish$),$ and the clerk serves customers at rate $3$ per hour. As soon as one queue is free you will be served. Note that the second customer in queue $2$ will not switch queue and will be served by the clerk of queue $2.$

Question $($a$)$ What is the probability that you will be served by the clerk in the first queue?

Question $($b$)$ What is the probability that you will start receiving service within the next $30$ minutes $($half an hour$)?$

Question $($c$)$ What is the expected time at which you will leave the post office after being served?