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 A B AB 1 0.082 0.102 0.005 0.004 Ethnic Group 0.139 0.141 0.018 0.009 3 0.215 0.202 0.063 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 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(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.) O If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A|C). OIf a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). OIf 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(A|C). OIf we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(CJA). O If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C|A). (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.)
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 A B AB 1 0.082 0.102 0.005 0.004 Ethnic Group 0.139 0.141 0.018 0.009 3 0.215 0.202 0.063 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 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(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.) O If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A|C). OIf a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). OIf 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(A|C). OIf we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(CJA). O If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C|A). (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.)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 7E: List the sample space of each experiment. Selecting a letter of the alphabet
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