Question: A post oce has 2 clerks. Alice enters the post oce while 2 other customers, Bob and Claire, are being served by the 2 clerks. She is next in line. Assume that the time a clerk spends serving a customer has the Exponential (λ) distribution.
(a) What is the probability that Alice is the last of the 3 customers to be done being served?
(b) What is the expected total time that Alice needs to spend at the post oce?