A manufacturing procedure produces 100 parts in batch. The probability the part is defective is 0.001. Supposing independence:
a. Determining the probability that there are fewer than 2 defective parts in a batch?
b. What is the expected number of batches until you observe a 3rd batch with two or more defective parts?
c. At the end of the day, 4 batches had been discarded for having too many faulty parts. In the 4 batches, there were a total of 50 faulty parts. If you select 20 parts at random without replacement from the discarded batches, what is the probability that you select 2 faulty parts?