Problem 51 It is known that in Canada the blood types have t

Problem 5.1. It is known that in Canada. the blood types have the following distribution: 46% O, 42% A, 9% B, 3% AB. A randomly chosen Canadian receives a blood transfusion. Knowing that O is a universal donor, A can donate only to A and AB, B can donate only to B and AB, and AB can donate only to AB, what is the probability that the transfusion is not successful?

Solution

Adding up the probabilities of unsuccessful transfusions,

P(unsuccessful) = P(A) P(donor is B or AB) + P(B) P(donor is A or AB) + P(O) P(donor is A, B, or AB)

P(unsuccessful) = P(A) [P(B) + P(AB)] + P(B) [P(A) + P(AB)] + P(O) [P(A) + P(B) + P(AB)]

= 0.3393 [ANSWER]