A major video distributor purchases blank DVDs from two sources: Retailer A whic

Question

A major video distributor purchases blank DVDs from two sources: Retailer A which provides 66% of the DVDs, and Retailer B, which provides the remaining 34%. Historically, 8% of the DVDs the video distributor purchased from Retailer A have been defective, whereas 9% of the DVDs purchased from Retailer B have been defective. A randomly selected DVD is found to be defective. Use Bayes' Theorem to determine the probability that the DVD came from Retailer A. The probability is (Round to three decimal places as needed.)

Explanation / Answer

P(A) = 0.66 , P(B) = 0.34

P(D/A) = 0.08 , P(D/B) = 0.09

P(A/D) = ?

P(A/D) = [P(A)*P(D/A)] / [ P(A)*P(D/A) + P(B)*P(D/B) ]

= 0.66*0.08 / [0.66*0.08 + 0.34*0.09]

= 0.0528/0.0834

= 0.633

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