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 2%. 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

P(Georgia) = 0.4

P(Ohio) = 0.6

P(defective | Georgia) = 0.05

P(defective | Ohio) = 0.02

P(defective) = P(defective | Georgia) * P(Georgia) + P(defective | Ohio) * P(Ohio)

                    = 0.05 * 0.4 + 0.02 * 0.6

                    = 0.032

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