A production process produces items in lots of 50. Sampling plans exist in which lots are pulled aside periodically and exposed to a certain type of inspection. It is usually assumed that the proportion defective in the process is very small. It is also important to the company that lots containing defects be a rare event. Currently the inspection plan by the company is to periodically sample randomly 10 out of the 50 in a lot and if none are defective, no intervention into the process is done.

(a) Suppose in a lot chosen at random, 2 out of 50 are defective. What is the probability that at least 1 in the sample of 10 from the lot is defective?

(b) From your answer in (a), comment about the quality of this sampling plan.

(c) What is the mean number of defects found out of 10?