45. Parts a,b,c posterior probability, a diagno EXERCISES Section 2.4 (45-69) 45

Question

45. Parts a,b,c posterior probability, a diagno EXERCISES Section 2.4 (45-69) 45. The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various 46 ethnic group-blood group combinations. Blood Group 0 AB 1 082 106 .008 004 47. Ethnic Group 2 .135 .141 018 006 3 .215 .200 .065 .020 Suppose that an individual is randomly selected from the population, and define events by A-type A selected), B= {type B selected), and C-ethnic group 3 selected). a. Calculate P(A), P(C), and P(A nC). b. Calculate both P(AIC) and P(CIA), and explain in context what each of these probabilities represents.

Explanation / Answer

a) P(A) = 0.103 + 0.141 + 0.2 = 0.447

P(C) =0.082 + 0.106 + 0.008 +....+0.02 = 1

P(A and C) = 0.103 + 0.141 + 0.2 = 0.447

b) P(A/C) = P(A and C) / P(C) = 0.447 / 1 = 0.447

P(C/A) = P(A and C) / P(A) = 0.447 / 0.447 = 1

c) P(C/B) = P(C and B) / P(B) = (0.008+0.018+0.065) / (0.008+0.018+0.065) = 1

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