Finding an organ transplant match. One of the problems encountered with organ transplants is the body’s rejection of the transplanted tissue. If the antigens attached to the tissue cells of the donor and receiver match, the body will accept the transplanted tissue. Although the antigens in identical twins always match, the probability of a match in other siblings is .25, and that of a match in two people from the population at large is .001. Suppose you need a kidney and you have two brothers and a sister.
a. If one of your three siblings offers a kidney, what is the probability that the antigens will match?
b. If all three siblings offer a kidney, what is the probability that all three antigens will match?
c. If all three siblings offer a kidney, what is the probability that none of the antigens will match?
d. Repeat parts b and c, this time assuming that the three donors were obtained from the population at large.