Question

The distribution of blood types in the United States according to the “ABO classification” is O:45%, A:40%, B:11%, and AB:4%. Blood is also classified according to Rh type, which can be negative or positive and is independent of the ABO type (the corresponding genes are located on different chromosomes). In the U.S. population, about 84% are Rh positive.

Sample two individuals at random and find the probability that:

(a) both are A negative

(b) one of them is O and Rh positive, while the other is not

(c) at least one of them is O positive

(d) one is Rh positive and the other is not AB

(e) they have the same ABO type

(f) they have the same ABO type and different Rh types

Answer 1

P(O) = 0.45

P(A) = 0.40

P(B) = 0.11

P(AB)= 0.04

P(Rh Positive) = 0.84

P(Ph Negative) = 0.16

(a)
P(Both A Nagative) = (0.40 X 0.0.16)² = 0.0041

(b)

Person 1:

P(O & Rh Positive) = 0.45 X 0.84 = 0.288

Person 2:

P(Not O Positive) = 1 - 0.288 = 0.712

So,

P(One of them is O and Rh positive , while other is not) = 0.288 X 0.712 = 0.2051

(c) P(at least one of them is O positive) = 1 - P(Both of them Not O Positive)

                                                         = 1 - 0.712² = 0.4931

(d) P(one is Rh positive & the other is Not AB) = 0.84 X 0.96 = 0.8064

(e) P(Same ABO Type) = 0.45² + 0.40² + 0.11² + 0.04² = 0.2025 + 0.16 + 0.0121 + 0.0.0016 = 0.3762

(f) P(Same ABO Type & Different Rh types) = P(Same ABO Type) - P(Same ABO Types & Same Rh types) = 0.3762 - [ (0.3762 X (0.84² + 0.16²)]

= 0.3762 - [ 0.3762 X 0.7312] = 0.1011