Question 5.335

122. Acceptance Sampling. You are in charge of purchasing for a large computer retailer. Your wholesaler delivers computers to you in batches of 100. You either accept or reject an entire batch based on a random sample of two computers: if both computers you sample are defective, then you reject the entire batch. Suppose that (unknown to you, of course) there are 10 defective computers in the batch of 100 computers.

  1. Should you conduct your sampling with or without replacement? Why?
  2. What is the probability that the first computer you select is defective?
  3. What is the probability that the second computer you select is defective, given that the first was defective, if you sample without replacement?
  4. What is the probability that you will accept the batch?
  5. What is the probability that you will reject the batch?