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c. Suppose that the defective rates of two factories ? and ? are 1% and 2%,...

c. Suppose that the defective rates of two factories ? and ? are 1% and 2%, respectively. One device is randomly selected from a batch of products with 60% products from ? and 40% products from ?. If it is found to be defective, what is the probability of the defective product being produced by factory ??

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Answer #1

P(A) = 0.60 , P(B) = 0.40

P(defective | A) = 0.01 , P(Defective | B) = 0.02

Using Bayes' theorem,

P(A | defective) = P(A) * P(defective | A) / [ P(A) * P(defective | A) + P(B) * P(defective | B) ]

= 0.60 * 0.01 / [ 0.60 * 0.01 + 0.40 * 0.02 ]

= 0.4286

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