The population of a particular country consists of three eth- nic 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 0 A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 215 200 .065 .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(AC). b. Calculate both P(A|C) and P(C|A), and explain in con- text what each of these probabilities represents. c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?

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The population of a particular country consists of three eth-
nic 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
0
A
B
AB
1
.082
.106
.008
.004
Ethnic Group
2
.135
.141
.018
.006
3
215
200
.065
.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(AC).
b. Calculate both P(A|C) and P(C|A), and explain in con-
text what each of these probabilities represents.
c. If the selected individual does not have type B blood, what
is the probability that he or she is from ethnic group 1?
Transcribed Image Text:The population of a particular country consists of three eth- nic 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 0 A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 215 200 .065 .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(AC). b. Calculate both P(A|C) and P(C|A), and explain in con- text what each of these probabilities represents. c. If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?
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