The number of defective components produced by a certain process in one day has a Poisson
distribution with mean of 20. Each defective component has probability of 0.60 of being
repairable.

(a) Find the probability that exactly 15 defective components are produced.
(b) Given that exactly 15 defective components are produced, find the probability that
exactly 10 of them are repairable.
(c) Let N be the number of defective components produced, and let X be the number of
them that are repairable. Given the value of N, what is the distribution of X?
(d) Find the probability that exactly 15 defective components are produced, with exactly 10
of them being repairable.