Automobiles arrive at a vehicle equipment inspection sta- tion according to a Poisson process with rate a = 10 per hour. Suppose that with probability 5 an arriving vehicle will have no equipment violations.

a. What is the probability that exactly ten arrive during the hour and all ten have no violations?

b. For any fixed y 10, what is the probability that y arrive during the hour, of which ten have no violations?

c. What is the probability that ten "no-violation" cars arrive during the next hour? [Hint: Sum the probabilities in part

(b) from y = 10 to *.]