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 B AB 1 0.082 0.108 0.009 0.004 Ethnic Group 2 0.133 0.141 0.018 0.005 0.215 0.190 0.075 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 P(A), P(C), and P(A N C). (Enter your answers to three decimal places.) P(A) = P(C) = P(A N C) = (b) Calculate both P(A|C) and P(CJA). (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.) O If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). O If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C|A). O If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C|A). O If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(C|A).