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 0.114 0.011 0.004 Ethnic Group 2 0.127 0.141 0.018 0.003 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 3 selected}. (a) Calculate P(A), P(C), and P(A n C). (Enter your answers to three decimal places.) P(A) = 0.457 P(C) - 0.5 P(A n C) - 0.202 (b) Calculate both P(A|C) and P(CJA). (Round your answers to three decimal places.) P(A|C) = 0.404 P(CIA) - 0.442 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(CJA). O If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(CIA). O If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). V 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). O If a person has type B blood, the probability that he is from ethnic group 3 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(A|C). (c) If the selected individual does not have type blood, what is the probability that he or she is from ethnic group 1? (Round your answer to three decimal places.) 0.481
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 0.114 0.011 0.004 Ethnic Group 2 0.127 0.141 0.018 0.003 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 3 selected}. (a) Calculate P(A), P(C), and P(A n C). (Enter your answers to three decimal places.) P(A) = 0.457 P(C) - 0.5 P(A n C) - 0.202 (b) Calculate both P(A|C) and P(CJA). (Round your answers to three decimal places.) P(A|C) = 0.404 P(CIA) - 0.442 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(CJA). O If we know that the individual came from ethnic group 3, the probability that he has type A blood is given by P(CIA). O If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A|C). V 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). O If a person has type B blood, the probability that he is from ethnic group 3 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(A|C). (c) If the selected individual does not have type blood, what is the probability that he or she is from ethnic group 1? (Round your answer to three decimal places.) 0.481
Transcribed Image Text: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
В
AB
1
0.082
0.114
0.011
0.004
Ethnic Group
2
0.127
0.141
0.018
0.003
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 3 selected}.
(a) Calculate P(A), P(C), and P(A n C). (Enter your answers to three decimal places.)
P(A)
0.457
P(C) =
0.5
P(A n C) =
0.202
(b) Calculate both P(A|C) and P(C|A). (Round your answers to three decimal places.)
P(A|C) =
0.404
P(C|A)
0.442
Explain in context what each of these probabilities represents. (Select all that apply.)
V If a person has type A 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 blood 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(A|C).
V 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).
O If a person has type B blood, the probability that he is from ethnic group 3 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(A|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.)
0.481
O O
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