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}.

Which of these probabilities represents. (Select all that apply by T or F.)

_T or F____If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C).

_T or F____If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C | A).

_T or F____If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C).

_T or F____If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A | C).

_T or F____If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(C | A).

_T or F____If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C | A).

Blood Group O A B AB 1 0.082    0.100     0.010    0.004 Ethnic Group 2 0.141    0.141    0.018 0.004 3 0.215    0.204    0.061 0.020

Explanation / Answer

If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C) -- False (F)

If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C | A) -- True (T)

If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C) - True (T)

If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A | C) -- False (F) (it will be P(C|B))

If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(C | A) -- False (F)

If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C | A) -- False (F) (it will be P(C|B))

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