Amari purchased 200 chips for her Capstone project from supplier A, 300 chips fr

Question

Amari purchased 200 chips for her Capstone project from supplier A, 300 chips from supplier B, and 500 chips from supplier C. Prior studies found that the conditional probabilities of chips from these suppliers being defective are as follows: P[Chip is defective | it came from Supplier Al 0.10 P[Chip is defective | it came from Supplier B]-0.08 P[Chip is defective | it came from Supplier C]-0.06 Amari mixed the chips from all suppliers together and randomly selected one chip. What is the probability that the selected chip is from supplier A? What is the probability that the selected chip is from supplier B? What is the probability that the selected chip is from supplier C? What is the probability that the selected chip is defective? Given that the selected chip is defective, what is the probability that it came from supplier B?

Explanation / Answer

a) P(Supplier A) = 200 / 1000 = 0.2

b) P(Supplier B) = 300 / 1000 = 0.3

c) P(Supplier C) = 500 / 1000 = 0.5

d) P(defective) = P(defective | Supplier A) * P(Supplier A) + P(defective | Supplier B) * P(Supplier B) + P(defective | Supplier C) * P(Supplier C)

= 0.1 * 0.2 + 0.08 * 0.3 + 0.06 * 0.5

= 0.074

e) P(supplier B | defective) = P(defective | Supplier B) * P(Supplier B) / P(defective)

= 0.08 * 0.3 / 0.074

= 0.324

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