Let X be the number of customers of a car salesman over a one-day period. Suppose that X has a Poisson distribtution with parameter \lambda = 3. Furthermore, suppose that one customer in five, on average, buys a car ( on a given visit), independently of the other customers. Let Y be the number of cars sold by the salesman in one day.
a) Given that the salesman had five customers during a given day, what is the probability that he sold exactly two cars?
b) What is the average number of cars sold by the saleman in a one-day period?
c) What is the probability that the salesman sells no cars during a given day?
Know that the salesman sold no cars during a given day, what is the probability that he had no customers?