Suppose 3 machines A, B and C in a manufacturing plant produce the same product

Question

Suppose 3 machines A, B and C in a manufacturing plant produce the same product and store in a warehouse. Of the total production, percent share for 3 machines A, B and C are 55%, 30% 15% respectively. The defective items produced by the 3 machines A, B and C are 4%, 3% and 2% respectively. For the purpose of quality control, an item is selected at random from the total items produced during the day. (a). What is the probability that the selected item is defective? (b). Given that the item selected for inspection is defective, what is the probability that the item was produced by the machine A?

Explanation / Answer

A) P(selected item is defective) = 0.55 * 0.04 + 0.3 * 0.03 + 0.15 * 0.02 = 0.034

B) P(produced by machine A | the selected item is defective) = P( the item selected is defective | produced by machine A) * P(produced by machine A)/ P(the selected item is defective)

= 0.04 * 0.55/0.034 = 0.647

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