Question

2. Basic Properties of Probability. (30 points total) Human blood can be classified into the four blood types A, B, AB, and O, where: A indicates that only the A antigen is present. . B indicates that only the B antigen is present. . AB indicates both the A and B antigens are present O indicates neither antigen is present Suppose that for a population in the US, the probability of having the blood types A, B, and O is estimated to be: Pr(A) 0.44, Pr(B) 0.08, and Pr(O) 0.45, respectively. (a) Calculate the probability that a person has both A and B antigens (i.e., blood type AB). Are the blood types, A, B, AB, and O mutually exclusive? b) Calculate the probability that a person does not have the A antigen (c) Calculate the probability that a person is either blood type A or blood type o. d) What is the probability that you and a classmate are both blood type O7

Answer 1

TOPIC:Properties of probability.

27 Define the following events as - A: Only the A antigen is present; B; Only the B " " "; AB : Both A and B antigens are presente 0 Anty Neither antigen is presente. Given that, Pn(A) = 0.44, Pro (B) = 0.08, Pn (o) 20.45. (a) = above events are exhaustive, we since the must have Pa (A) +P(B) + Po(AB) + Palo) = 1. * 0.044 +0.08 +P (AB) +0.45 = 1. Po(Ab) = 0.03.COM => Yes, the bolood types A, B, AB and o are mutually exclusive (ie. disjoint); since, a person can't have two types of blood groups at the same time,

6 we need => Pr ( does not have the A antigen). = Pn (only B a on o antingens are presents), = Pop (Bu). = Pip (B) + Po(o). " disjoint) cares events = 0 + 08 t 0.45. = 10.53) Buss o we needs - Pr (either blood type A er blood type o) = Pis (Au). Po () troco). Es bestellen = 0.44 +0.45 =10,89 coms since, Pn (0) = 0.45. and we needs Pp (both have blood type of since the blood groups of you and = Pp (0) x Pn (0) Your friend, are 0.45 X 0.45 = [0, 2025 Einss independent ]