Our company has two production facililties: one in Georgia and one in Ohio. The

Question

Our company has two production facililties: one in Georgia and one in Ohio. The Georgia plant produces 40% of our total output, and the Ohio plant produces the remaining 60%. Some of our products have proven to be defective. Of the items produced in Georgia, 5% are defective; at our Ohio plant the defect rate is 12%. Suppose an item produced by our company is selected at random (there is a 40% chance it came from Georgia, for example).

What is the probability that it will be defective? Give your answer as a decimal fraction to at least three places

Explanation / Answer

G- Georgia, O-Ohio. D- Defective

P(D/G) = P(Defective provided it came from georgia)

P(G) = 0.4

P(O) = 0.6

P(D/G) = 0.05

P(D/O) = 0.12

P(D) = P(G)*P(D/G) + P(O)*P(D/O) = 0.4*0.05 + 0.6*0.12 = 0.020+0.072 = 0.092

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