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. Blood Group 0 AB 1 0.082 0.114 0.007 0.004 Ethnic Group 2 0.127 0.141 0.018 0.007 3 0.215 0.203 0.062 0.020 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 PA), PC), and PIA nC). (Enter your answers to three decimal places.) p(C) = PLA n C) = (b) Calculate both PIA I C) and PC I A). (Round your answers to three decimal places.) p(A | C)= Explain in context what each of these probabilitles represents. (Select all that apply.) If a person has type B blood, the probability that he is from ethnic group 3 is given by PIA I c). If we know that the individual came from ethnic group 3, the probability that he has type A is given by p(CI A). If a person has type A blood, the probability that he is from ethnic group 3 ls 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) 1f we know that the individual came from ethnic group 3, the probability that he has type A is given by P( If a person has type A blood, the probability that he is from ethnic group 3 is given by P( C). C). (c) If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1? (Round your answer to three decimal places.) Need Help?RadItTalk to a Tutor

Explanation / Answer

a)

P(A) =0.458

P(C) =0.5

P(A n C) =0.203

b) P(A|C) =P(A nC)/P(C) =0.203/0.5 =0.406

P(C|A )=P(A n C)/P(A) =0.203/0.458 =0.443

3rd and 5th option is correct

c)

probability =(0.207-0.007)/(1-0.087)= 0.219

O A B AB total 1 0.082 0.114 0.007 0.004 0.207 2 0.127 0.141 0.018 0.007 0.293 3 0.215 0.203 0.062 0.02 0.5 total 0.424 0.458 0.087 0.031 1

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