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(a) A post office has two clerks. After three people, A, B, and C, enter simultaneously, A and B go directly to the clerks and C waits until either A or B leaves before she begins service. What is the probability that A is still in the post office after B and C have left when the service times are independent and exponentially distributed with rate 1? Let X1, X2, X3 be i.i.d. exponential random variables, each with rate 1. Show that: (b) P(X1