Question

Suppose you have just received a shipment of 27 modems. Although you​ don't know​ this, 3 of the modems are defective. To determine whether you will accept the​ shipment, you randomly select 8 modems and test them. If all 8 modems​ work, you accept the shipment.​ Otherwise, the shipment is rejected. What is the probability of accepting the​ shipment?

Answer 1

Let the random variable denote the number of defective modems. The random variable follows the Binomial distribution.

In a shipment of 27 items, 3 modems are defective. Therefore, the probability of obtaining a defective modem, say , is:

The number of modems to be tested is .

Therefore, follows the Binomial distribution with and .

The shipment will be accepted in case none of the inspected items is defective, that is, the following probability needs to be determined:

RESULT:

The probability of accepting the shipment is .