The population of a particular country consists of three ethnic groups. Each ind

Question

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 ethnic group-blood group combinations. 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}. Calculate P(A), PC), and P(A Intersection C). (Enter your answers to three decimal places.) P(A) = _____ P(C) = _____ P(A Intersection C) = ______ Calculate both P(A | C) and P(C | A). (Round your answers to three decimal places.) P(A | C) = ______ P(C | A) = ______ Explain in context what each of these probabilities represents. (Select all that apply.) If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(C | A). If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C | A). If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C). If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A | C). If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C). If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C | A). If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1? _______

Explanation / Answer

please check below table if any error is there please revert cause in picture it is blurry.

a)P(A)=0.46

P(C)=0.5

P(AnC)=0.2

b)

P(A|C)=0.2/0.5=0.4

P(C|A)=0.2/0.46=0.435

these two are correct: 3rd and 6th one

if we know that individual came from ethnic group 3 ; the probabilty........by P(A|C)

if a person has type A blood; the probability..............P(C|A)

c)

probability=(0.082+0.119+0.004)/(0.419+0.46+0.03)=0.226

blood group ethnic Group O A B AB total 1 0.082 0.119 0.008 0.004 0.213 2 0.122 0.141 0.018 0.006 0.287 3 0.215 0.2 0.065 0.02 0.5 Total 0.419 0.46 0.091 0.03 1

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