Question

A shipment of 70 laptops, including 7 that are defective, is sent to a retail store. The receiving department selects 9 at random for testing and rejects the whole shipment if 1 or more in the sample are found to be defective. What is the probability that the shipment will be rejected? C(10,3) may be written to express 10 choose 3, and P(10,3) may be written to express 10 permute 3.

Answer 1

The probability that the shipment will be rejected is approximately 37.96%.

Step-by-step explanation:

To find the probability that the shipment will be rejected, we need to find the probability that at least one defective laptop is chosen in the sample of 9 laptops. We can use the concept of the hypergeometric distribution to solve this problem.

The probability that a laptop is defective is 7/70 since there are 7 defective laptops out of 70 total laptops in the shipment. The probability that a laptop is not defective is 63/70.

Using the hypergeometric distribution formula, the probability that 0 defective laptops are chosen in the sample is P(X=0) = (C(7,0)*C(63,9))/(C(70,9)) ≈ 0.6204. Therefore, the probability that the shipment will be rejected is approximately 1 - 0.6204 = 0.3796, or 37.96%.