This problem continues with the discussion of ABO blood groups of Problem 4.9. W

Question

This problem continues with the discussion of ABO blood groups of Problem 4.9. We now consider the black and Caucasian population of the United States. Approximately 20% of the U.S. population is black. This produces the following two-way classification of race and blood type:

Blood Group

This table specifies, for example, that the probability is 0.352 that a person selected at random is both Caucasian and blood group A.

(a) Are the events “blood group A” and “Caucasian race” statistically independent?

(b) Are the events “blood group A” and “Caucasian race” mutually exclusive?

(c) Assuming statistical independence, what is the expected probability of the event “blood group A and Caucasian race”?

(d) What is the conditional probability of “blood group A” given that the race is Caucasian?

A B AB O Total Caucasian 0.352 0.064 0.024 0.360 0.80 American black 0.054 0.040 0.008 0.098 0.20 Total 0.406 0.104 0.032 0.458 1.00

Explanation / Answer

(a) The Events Blood Group A and Caucasian race are not Independent as P( A and caucassian race)=0.352 is not equal to P(Blood Group A)XP(caucasian Race)=0.406X0.80=0.324

(b)Since P( Bllod group A and caucasian race)=0.352 and hence non zero and so the events Blood Group A and Caucasian race are not mutually exclusive.

(c) Assuming Statistical Independence,P( Blood group A and  caucasian race )=P(Blood group A )XP( caucasian race)=0.406X0.80=0.324

(d) P( Event Blood Group A / The Event is a Caucasian race) = P(Blood Group A and Caucasian race) /P(Caucasian race)

=0.352/0.80=0.44

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