Blood Types of Ethnic Groups
This probability table concerns the blood types of three ethnic groups.
Type O Type A Type B Type AB Group X .082 .106 .008 .004 Group Y .135 .141 .018 .006 Group Z .215 .200 .065 .020 total .432 .447 .091 .030 If someone is in Group Z, what is the probability they have blood type A? We want to compute P(A | Z). By Bayes formula,
P(A | Z) = P(A ∩ Z)/P(Z). Clearly: P(A)= .447, P(Z)=.5, P(A ∩ Z)=.2
so P(A | Z) = P(A ∩ Z)/P(Z) = .2/.5 = 40%
Similarly,
P(Z | A) = P(Z ∩ A)/P(A) = .2/.447 ≈ .447 If an individual does not have blood type B, what is the probability this individual is in Group X?
We want: P(X | -B) = P(X ∩ -B)/P(-B). But
P(-B)= 1 - P(B) = 1 - .091 = .909 and P(X ∩ -B) = 0.82 + .106 + .004 = .192
so: P(X | -B) = .192/.909 ≈ .211 = 21.1%