A Restaurant Is About to Close, but It Must Wait

Essay

A restaurant is about to close, but it must wait until all 8 remaining customers have left. Starting now, each customer's remaining time in the restaurant is exponentially distributed with mean fifteen minutes. If the customers leave independently of one another, find the probability that
(a) after 2 hours the restaurant is still open;
(b) after 1 hour, the restaurant is still waiting on exactly 2 customers.