A bank has two tellers and they take an exponentially distributed time to deal with any customer. Let the parameters of these two service times be and respectively (assume independence).
You arrive to find exactly two customers present, each occupying a teller:
(a) You toss a fair coin and depending on the outcome you queue for one of the two tellers. What is the probability p that you are the last of the three customers to leave the bank?
(b) Suppose that you know and and you choose to be served by the quicker teller. What is p in this case?