19. 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 ìÁ, and  after an exponential time with rate ìÂ. New kidneys arrive in accordance with a Poisson process having rate A. It has been decided that the first kidney will go to A (or to  if  is alive and A is not at that time)

and the next one to  (if still living).

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

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