Automobiles Arrive at a Vehicle Equipment Inspection Station According to a Poisson

Essay

Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate $\alpha$ = 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 $y \geq 10$
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 $\infty ,$
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