A company buys components from two suppliers. One produces components that are o

Question

A company buys components from two suppliers. One produces components that are of higher quality than the other. The high-quality supplier, call it Supplier A, has a defect rate of 2%. The low-quality supplier, Supplier B, has a defect rate of 10% but offers lower prices. This company buys in equal volume from both suppliers, with half of the orders going to each supplier.

(a) What is the probability that a component to be installed is defective?

(b) If a defective component is found, what is the probability it came from Supplier A?

(c) Assume that two defective components were found from the same supplier, what is the probability that the components came from Supplier A?

Explanation / Answer

(a) P(A) = 0.02

P(B) = 0.1

combined probability = (P(A) + P(B))/2 = 0.06

(b)P(A|Defect) = P(defect|A)P(A)/P(Defect) = 0.02*(0.5)/0.06 = 0.01/0.06 =1/6

(c)P(two defective came from suplier A) = P(A|Defect)^2 = (1/6)^2 = 1/36

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