Brittany purchased 500 chips for her Capstone project from s

Brittany purchased 500 chips for her Capstone project from supplier A, 200 chips from supplier B, and 300 chips from supplier C. She tested the different chips in the lab and found the following conditional probabilities of a chip briny defective: P[Chip is defective i it came from Supplier A] = 0.05 P[Chip is defective i it came from Supplier B] = 0.10 P[Chip is defective i it came from Supplier C] = 0.10 Brittany mixed all the chips from the different s random What is the probability that the chip Brittany selected is defective? Given that the selected chip that Brittany selected is defective, what is the probability that it came from supplier B?

Solution

Let D = defective

a)

P(D) = P(A) P(D|A) + P(A) P(D|A) + P(A) P(D|A)

P(D) = (500/1000)*(0.05) + (200/1000)*(0.10) + (300/1000)*(0.10)

P(D) = 0.075 [ANSWER]

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b)

P(B|D) = P(B) P(D|B) / P(B)

= (200/1000)*0.10/0.075

= 0.266666667 [ANSWER]