A reservation service employs five information operators who receive requests for information independently of one another, each according to a Poisson process with rate a = 2 per minute.
a. What is the probability that during a given 1-min period, the first operator receives no requests?
b. What is the probability that during a given 1-min period, exactly four of the five operators receive no requests?
c. Write an expression for the probability that during a given 1-min period, all of the operators receive exactly the same number of requests.