Lot inspection sampling. Imagine that you are purchasing small lots of a manufactured product. If it is very costly to test a single item, it may be desirable to test a sample of items from the lot instead of testing every item in the lot.

Suppose each lot contains 15 items. You decide to sample 8 items per lot and reject the lot if you observe 1 or more defectives.

a. If the lot contains 1 defective item, what is the probability that you will accept the lot?

b. What is the probability that you will accept the lot if it contains 2 defective items?