A person enters a bank and finds all of the four tellers busy serving customers. There are no other customers in the bank, so the person will start receiving service as soon as one of the customers in service leaves. Customers have independent, identical, exponential distribution of service time with mean 1/μ.
a) What is the probability that the person will be the last to leave the bank assuming no other customers arrive? Explain your answer fully.
b) If the average service time is 1 minute, what is the average time the person spend in the bank?