Medicine and Clinical Studies When a person has a certain ty

Medicine and Clinical Studies When a person has a certain type of leukemia, a physician may perform a bone marrow transplant in order to restore a healthy blood supply. Among the general population, the chances of an acceptable bone marrow match are 1 in 20,000.^40 Suppose a person needs a bone marrow transplant and four people from the general population are selected at random. What is the probability that none of the four will match? What is the probability that at least one will match? How many people would have to be tested in order for the probability of at least one match to be 0.50?

Solution

X be the random variable denoting number of matches in bone marrow.

X follows a Binomial distrubution with n=4,p=1/20000

a)P(X=0)=0.9998

b)P(At least one will match)=1-P(No will match)=1-P(X=0)=0.0002

c)Near About 13875 persons are needed to be test so that probability of atleast one match is 0.5