A manufacturing firm employs three analytical plans for design and development o

Question

A manufacturing firm employs three analytical plans for design and development of a particular product. For cost reasons, all three plans are used at varying times. In fact, plans A, B, and C are used for 30%, 20%, and 50% of the products, respectively. It is also known from past experience that 2% of the products made using plan A will be defective. Similarly, the product defective rate for plan B and C are 3% and 1%, respectively. Suppose that a finished product is randomly selected. What is the probability that it will be defective? If a randomly selected product is found to be defective, which plan was most likely used? Clearly explain your answer.

Explanation / Answer

By using the Bayes Probability Law

(a) 0.017

(b) Plan C was most likely used.

Event Prior Prob. Conditional Prob. Joint Prob. Posterior Prob. A 0.3 0.02 0.006 0.3529 B 0.2 0.03 0.006 0.3529 C 0.5 0.01 0.005 0.2942 Total 0.017

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