In an acceptance sampling inspection, 10 items are drawn at random from a large lot with a defect rate of 5%, and the lot is accepted if none of them is defective. Which of the following is closest to the probability that this lot is accepted?

Answer: C. 0.60

Because the lot is large, each of the 10 items drawn can be regarded as good independently with a probability of 95%. The probability that all 10 are good is 0.95¹⁰ ≈ 0.60. Even a lot with a 5% defect rate is accepted about 60% of the time, so the sample size and acceptance criterion are chosen according to which defect rates should be rejected and with what probability.

• A. 1 − 0.95¹⁰ ≈ 0.40 is the probability that one or more defectives are found and the lot is rejected.
• B. This is 1 − 10 × 0.05 = 0.50, which simply adds the probabilities of finding a defective and so counts the cases with two or more defectives more than once.
• C. Correct. 0.95¹⁰ ≈ 0.60.