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4. An inspector working for a manufacturing company has a 95% chance of correctly identifying defective items and a 1% chance of incorrectly classifying a good item as defective. The company has evidence that 0.5% of the items its line produce are nonconforming. (a) What is the probability that an item selected for inspection is classified as defective? (b) If an tem selected at random is classified as defective, what is the probability that it is indeed nonconforming? c) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?

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a)P(classified as defective)=P(defective and classified as defective)+P(not defective and classified as defective)=0.005*0.95+(1-0.005)*0.01=0.01470

b)

P(defective given classified as defective)=P(defective and classified as defective)/P(classified as defective)

=0.005*0.95/0.01470=0.323129

c)

P(classified as non defective)=1-P(defective)=1-0.01470=0.9853

hence P(good given classified as non defective)=P(good and classified as non defective)/P(classified as non defective)

=0.995*0.99/0.9853=0.999746

hence P(good given

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