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 in the various ethnic group-blood group combinations. Blood Group B AB 0.082 0.108 0.007 0.004 Ethnic Group 0.133 0.141 0.018 0.007 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(AN 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(CIA) = Explain in context what each of these probabilities represents. (Select all that apply.) 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). 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). 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 blood 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.)
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 in the various ethnic group-blood group combinations. Blood Group B AB 0.082 0.108 0.007 0.004 Ethnic Group 0.133 0.141 0.018 0.007 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(AN 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(CIA) = Explain in context what each of these probabilities represents. (Select all that apply.) 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). 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). 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 blood 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.)
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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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 indiv
in the various ethnic group-blood group combinations.
Blood Group
A
B
AB
1
0.082
0.108
0.007
0.004
Ethnic Group
0.133
0.141
0.018
0.007
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) =
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(CJA) =
Explain in context what each of these probabilities represents. (Select all that apply.)
O If 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 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 B blood, the probability that he is from ethnic group 3 is given by P(A|C).
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(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.)
Expert Solution
Step 1 : Introduction
Probability :
Probability may be a discipline of arithmetic involved with numerical explanations of the chance of an incident occurring or the reality of a claim.
The chance of an incident may be a variety between zero and one, with zero indicating impossibility and one indicating certainty, broadly.
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