Question

Blood GroupO A B ABEthnic Group 1)0.082 0.101 0.005 0.0042)0.140 0.141 0.018 0.0093)0.215 0.195 0.070 0.020Explain 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 we know that the individual came from ethnic group 3, the probability that he has type A is given by P(C | A).If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C | A).If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C | A).If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C).If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A | C).

Answer 1

P (A|C) = 0.39

P (C|A) = 0.446

Explanation:

The data provided is as follows:

Blood Group

O A B AB Total

1) 0.082 0.101 0.005 0.004 0.192

Ethnic Group 2) 0.140 0.141 0.018 0.009 0.578

3) 0.215 0.195 0.070 0.020 0.500

Total 0.437 0.437 0.093 0.033

The event C = {Ethnic group 3 is selected}

Compute the value of P (A|C) as follows:

`P(A|C)=(P(A\cap C))/(P(C))=(0.195)/(0.5)=0.39`

If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C) = 0.39.

Compute the value of P (C|A) as follows:

`P(C|A)=(P(A\cap C))/(P(A))=(0.195)/(0.437)=0.446`

If we know that the individual has type A blood group, the probability that he came from ethnic group 3 is given by P(C | A) = 0.446.