Math 3680 Homework 2 x G A woman ued a compu C wwwweba ssign

Math 3680 Homework 2 x G A woman ued a compu C www.weba ssign.net/web/Student/Assi Responses/submit?dep 15568135 ignment The population of a partioular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups The accompanying joint p table gives the proportions of individuals in the various ethnic group-blood group combinations. Blood Group 1 0.082 0.118 0.011 0.004 Ethnic Group 2 o 121 o.141 o 018 0.003 3 0.215 0.205 0.060 0.020 suppose that an individual is randomly selected from the population, and define events by A Ktype A selected). a ktype B selected), and c-(ethnic group 2 selected). (a) calculate POA), PKc). and POA n c). (Enter your answers to three decimal places.) (b) Calculate both PAIC and PKCIA). (Round your answers to three decimal places.) PICIA)\" Explain in context what each of these probabilties represents. (Select all that apply. If a person has type A blood, the probabilty that he is from ethnic group 3 is given by AC If we know that the individual came from ethnic group 3, the probabilty that he has type A is given by p(CIA) If a person has type B blood, the probability that he is from ethnic group 3 is given by ACIA). If we know that the individual came from ethnic group 3, the probabilty that he has type A is given by PMA lo if a person has type A blood, the probability that he is from ethnic croup 3 is given by p A IC). o If a person has type e blood, the probability that he is from ethnic oroup 3 isgiven by AAIC) (c) If the selected individual does not have type B blood, what is the probabaty that he or she is from ethnic group (Round your answer tothree deon alplaces.)

Solution

P(A) = 0.118+0.141+0.205 = 0.464

P(C) = 0.082+0.123+0.215+0 118+0.141+0.205+0.011+0.018+0.060+0.04+0.003+0.020= 1

P(A int C ) = P(A) + P(C) - P(A U C )= 0.464+1-1=0.464

P(A|C) = P(A int C)/P(C) = 0 464/1 = 0.464

P(C|A) = P(A int C)/P(A) = 0.464/0 464 =1

c) if a person is not of blood group B and is not from ethnic group 3 .. its probability is = 0.082+0.123+0.118+0.141+0.004+0.003=0.471

b) if a person is of type A then probability that he is fron ethnic grp 3 is give by P(C|A)

If a person is from ethnic group 3 and has blood group A is given by P*A|C)

And the other parts can be done simularly

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