he population of a particular country consists of thrce cthnic groups. Each indi
ID: 3351850 • Letter: H
Question
he population of a particular country consists of thrce cthnic groups. Each individual bclongs to one of the four mafor blood groups. The accompanying joint probability table gives the proportions of individuals in the varlous ethnic group-blood group combinations. Blood Group 0 AB 1 0.082 0.105 0.009 0.001 Ethnic Group 2 0.136 0,141 0.018 0.005 3 0.215 0.206 0.059 0.020 Suppose that an individual i5 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 PIA nC. (Enter your answers to three decimal places.) P(A) = (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 probabilitles represents. (Select all that apply.) If we know that the individual came from ethnic group 3, the probability that he has type A is given by P( A). If a person has type A blood, the probability that he is from ethnic group 3 is given by PA 1 C). 1f we know that the individual came from ethnic group 3, the probability that he has type A is given by p( If a person has type B blood, the probability that he is from ethnic group 3 is given by (Cl A). If a person has type A blood, the probability that he is from ethnic group 3 is given by PC ! If a person has type B blood, the probability that he is from ethnic group J is given by q, (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.)Explanation / Answer
a)
P(A)=0.105+0.141+0.206 =0.452
P(C)=0.215+206+0.059+0.02=0.5
P(AnC) =0.206
b) P(A|C) =0.206/0.5=0.412
P(C|A) =0.206/0.452=0.456
if we knew that someone from ethnic group 3 ; the probability that he has type A is given by P(A|C)
if someone has ttype A blood; the probability that he is from ethnic group 3 is is given by P(C|A)
c)
probability =(0.082+0.105+0.004)/(1-0.009-0.018-0.059)=0.209
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