The population of a particular country consists of three ethnic groups. Each ind

Question

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 individuals in the various ethnic g roup -bloo d group combinations Blood Group 0.082 0.136 0.215 0.105 0.141 0.200 0.007 0.018 0.065 AB 0.004 0.007 0.020 Ethnic Group 3 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) P(A) = (b) Calculate both P(A | C) and p(C | A) RAIC) Explain in context what each of these probabilities 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 | C). If a person has type A blood, the probability that he is from ethnic group 3 is given by P( A) If a person has type B blood, the probability that he is from ethnic group 3 is given by P( A) 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 B blood, the probability that he is from ethnic group 3 is given by P(A | C) If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C)

Explanation / Answer

from above blow is joint probability distribution:

a)P(A)=0.4460

P(C)=0.500

P(A n C)=0.2000

b)P(A|C)= P(A n C)/P(C) =0.2/0.5 =0.4

P(C|A) =P(A n C)/P(A) =0.2/0.446 =0.4484

1 st option is correct

2nd option is correct

c)probability =(0.082+0.105+0.004)/(1-0.09)=0.2099

blood group ethnic group O A B AB Total 1 0.0820 0.1050 0.0070 0.0040 0.1980 2 0.1360 0.1410 0.0180 0.0070 0.3020 3 0.2150 0.2000 0.0650 0.0200 0.5000 Total 0.4330 0.4460 0.0900 0.0310 1.0000

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