9. Vincent is a patient with the life threatening blood cancer leukemia, and he is in need of a bone marrow transplant. He asks n people whether or not they are willing to donate bone marrow to him if they are a close bone marrow match for him. Suppose that each person’s response, independently of others, is positive with probability p1 and negative with probability 1−p1. Furthermore, suppose that, independently of the others, the probability is p2 that a person tested is a close match.

(a) Find the probability that Vincent finds at least one close bone marrow match among these n people.

(b) Suppose that the probability is 1 in 10,000 that two unrelated persons are compatible; that is, have a close bone marrow match. If 70% of the people asked would respond positively to Vincent’s request, and he asks 1000 people, what is the probability that he will find a match?What if he asks 100,000 people?