An inspector working for the manufacturing company has a 99% chance of properly identifying defective items and a .5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces .9% of nonconforming items.
a) What is the probability that the item selected for inspection is confidential as defective?
b) If an item chosen at random is classified as non-defective, what is the probability that it is indeed good?