Two individuals, A and B, both require kidney transplants. If she does not re- ceive a new kidney, then A will die after an exponential time with rate u A, and B after an exponential time with rate uB. New kidneys arrive in accordance with a Poisson process having rate .. 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). 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? (а)

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