I have a problem that says "Automobiles arrive at a vehicle equipment inspetion station according to a Poisson process with a rate α=10 α=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 al 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?
for a) I have p(X≥`10) = p^x ((e^-l)(l^x)/x!) which gives 0.000122178
I am lost with how to set up b and c, and I feel like b is in the form of P(y arrive and exactly 10 have no violations) = P(exactly 10 have no violations | y arrive) ⋅ P(y arrive) but very confused because I don't know what y is, but is the question asking for a numeric answer or just a formula?