According to a study, one-seventh of all rough diamonds produced in one region a

Question

According to a study, one-seventh of all rough diamonds produced in one region are blood diamonds. Also, 88% of the region's rough diamonds are processed in City X, and of these diamonds, one-fourth are blood diamonds. a. Find the probability that a rough diamond produced in this region is not a blood diamond. b. Find the probability that a rough diamond is processed in City X and is a blood diamond. a. The probability that a rough diamond produced in this region is not a blood diamond is (Simplify your answer. Type an integer or a fraction.) b. The probability that a rough diamond is processed in City X and is a blood diamond is Simplify your answer. Type an integeror a fraction.)

Explanation / Answer

A: blood diamond

B: processed in city X

We are given that P(A)=1/7, P(B)=0.88, P(A|B)=1/4

a) P(not A)=1-P(A)=1-(1/7)=6/7

b) P( A and B)=P(A|B)*P(B)= (1/4)*(0.88) =0.22 or 11/50

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