Two individuals, A and B, both require kidney transplants. If she does not receive a new kidney, then A will die after an exponential time with rate μA, and B after an exponential time with rate μB. New kidneys arrive in accordance with a Poisson process having rate λ. It has been decided that the first kidney will go to A (or to B if B is alive and A is not at that time) and the next one to B (if still living).

(a) What is the probability that A obtains a new kidney?

(b) What is the probability that B obtains a new kidney?

(c) What is the probability that neither A nor B obtains a new kidney?

(d) What is the probability that both A and B obtain new kidneys?

(e) Find the expected time until neither A nor B is waiting.