All human blood can be \"ABO-typed\" as one of O, A, B, or AB, but the distribut

Question

All human blood can be "ABO-typed" as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in a country:

(a) What is the national probability of type O blood?

(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from this country can donate blood to Maria?

Explanation / Answer

a) Total probability is 1 always

P(A) + P(B) + P(AB) + P(O) = 1

So P(O) = 1 - 0.4 - 0.11 - 0.03

P( O ) = 0.46

the national probability of type O blood is 0.46

b)   Maria has type B blood.

So she can safely receive blood transfusions from people with blood types O and B.

We want to find the probability that a randomly chosen person from this country can donate blood to Maria from the given frequency distribution.

Since blood groups are mutually exclusive because one person dose not have two blood groups.

So required probability obtained by adding probabilities of B and O

So required probability = 0.11 + 0.46 = 0.57

the probability that a randomly chosen person from this country can donate blood to Maria is 0.57

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