1) Dr. Hayes goes to a bookstore to purchase a new book. However when she gets to the checkout (that is, when she enters the checkout system) she finds that Dr. Cox is being served by clerk 1 and Dr. Browne is being served by clerk 2. There are only 2 clerks at the store. Dr. Hayes is told that her service will begin as soon as either Dr. Cox or Dr. Browne leaves the store. If clerk i serves at an exponential rate i, i = 1, 2, what is the probability that, of the three customers, Dr. Hayes is the last one to leave the store?

2) Suppose that you arrive at the single-clerk post office to send a package and find one customer being helped and another 4 customers waiting in line. You join the end of the line. If the service times are all exponential with rate , what is the expected amount of time you will spend at the post office (assume customers are helped one at a time, and you will leave the post office as soon as your package is sent)?