The populatlon of a particular country consists of three ethnic groups. Each Ind

Question

The populatlon of a particular country consists of three ethnic groups. Each Individual helongs to ane of the four major blood groups. The accompanying joinr probability table gves the proportions of Indviduals in the varlous ethnic g Blood Group 1 0.082 0.10 0.00a 0.004 .14D 0.141 0.018 0.0aG 0.215 0.2D1 0.0 0.020 Fthnic Group Suppose that an individual is randomly sclacted from the population, and define avents by typc A sclected, -type B selectod, and C-ethnic group 3 solected) (a) Calculata PA), PC,and PAnC). (Entar your answers to thran decimal placas.) Anc) b) Caleulate bath PA C) and PCIA). (Raund your answers to threa decimal places Explain in contaxt what each af thasa prohabilities reprasents. (Salect all that apply.) If a person has type B blood, the probability that he is from ethnic group 3 is given by PIA | c) If a person has type B blood, the prohability that he is from ethnic group 3 ls glven by PC IA). If a persan has type A blnod, the prohability that ha is from ethnic group 3 is given by PA I c). If person has type A blood, the probability that he is fom ethnic group 3 is given by prc l A). If we know that the individual came from athnic group 3, the probability that he has typa A is givan by PA IC) l It we know that the individual came from ethnic group 3, the probability that he has type A is given by PiCI A) (c) It the selected individual does not have type B blood, what is the probability that he or she is trom ethnic group 1? (Round your answer to three deimal places.)

Explanation / Answer

Ans:

a)

P(A)=0.101+0.141+0.201=0.443

P(C)=0.215+0.201+0.064+0.02=0.500

P(A and C)=0.201

b)

P(A/C)=P(A and C)/P(C)=0.201/0.5=0.402

P(C/A)=P(A and C)/P(A)=0.201/0.443=0.454

Fourth and fifth options are correct.

c)

P(does not have type B)=1-0.090=0.910

P(Group 1/does not have type B)=(0.082+0.101+0.004)/0.910=0.187/0.910=0.210

O A B AB Total 1 0.082 0.101 0.008 0.004 0.195 2 0.140 0.141 0.018 0.006 0.305 3 0.215 0.201 0.064 0.020 0.500 Total 0.437 0.443 0.090 0.030 1.000

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