An automated engine valve inspection system used by a valve manufacturing compan

Question

An automated engine valve inspection system used by a valve manufacturing company has a 99% .chance of correctly identifying defective engine valves and a 0.5% chance oflncorrectly classifying a good valve as defective. The company produces 0.9% defective items. Probability that a valve is classified defective = P(D), the probability that a valve is good = P(G). What is the probability that a single item selected for inspection is classified as defective, P(D) =? If a valve selected at random is classified by the automated system as not defective (D'), what is the probability that is indeed good = P(G|D')?

Explanation / Answer

a) P ( D) = P ( Good but incorrectly classified) + P ( Defective and correctly classified)

= (0.991 * 0.005) + (0.009 * 0.99)

= 0.013865

= 1.3865%

b)

P ( G) = P ( Good and correctly identified) + P ( defective but wrongly identified)

= (0.991 * 0.99) + ( 0.009 * 0.005)

= 0.981135

= (0.991 * 0.99) / 0.981135

= 0.9999

Hope this helps.

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