A post office has 2 clerks. Alice enters the post office 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(x) distribution.
(a) What is the probability that Alice is the last of the 3 customers to be done being served Hint: no integrals are needed.
(b) What is the expected total time that Alice needs to spend at the post office?
I understand that no matter who leaves the office first, the remainer has the same expo(x) like Alice, but don't have intuitive thinking why the answer for the 1st is 1/2.