Question

An inspector has a 99%chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 0.9% of non-conforming items.

Define event A: an item is actually conforming the requirement (i.e. a good part)

Define even B: an item is classified as defective

a) what is the probability that a defective item is incorrectly classified as a non-defective one? Write down the mathematical presentation and provide its value

b) what is the probability that an item selected for inspection is classified as defective?

Answer 1

a)

P(B^c|A^c) =1-P(B|A^c) =1-0.99 =0.01

b)

P(B) =P(A)*P(B|A)+P(A^c)*P(B|A^c) =(1-0.009)*0.005+0.009*0.99 =0.013865