A factory tests all its products. The proportion of defective items is 0.01. The

Question

A factory tests all its products. The proportion of defective items is 0.01. The probability that the test will catch a defective product is 0.95. The test will also reject nondefective products with probability 0.01. (a) Given that a product passes the test, what is the probability that it is defective? Probability test catches defective product = 0.95, Probability test rejects a nondefective product = 0.01 (b) Given that the product does not pass the test, what is the probability that the product is defective?

Explanation / Answer

a)P(passes the test)=P(non-defective and passes)+P(defective and passes)

=(1-0.01)*(1-0.01)+0.01*(1-0.95)=0.9806

therefore P(Defective given passes the test)=P(defective and passes)/P(passes the test)

=0.01*(1-0.95)/0.9806 =0.00051

b)

P(not passes)=1-P(passes)=1-0.9806=0.0194

therefore P(defective|not passes)=P(defective and not passes)/P(not passes)

=0.01*0.95/0.0194=0.489691

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