Question

Suppose you have just received a shipment of 22 modems. Although you​ don't know​ this, 4 of the modems are defective. To determine whether you will accept the​ shipment, you randomly select 5 modems and test them. If all 5 modems​ work, you accept the shipment.​ Otherwise, the shipment is rejected. What is the probability of accepting the​ shipment?

Answer 1

Of the 22 modems, 4 are defective and 18 are non-defective,

P(Accepting shipment) = P(all 5 modems work)

5 non-defective modems can be selected from 18 non-defective modems by ¹⁸C₅ ways.

¹⁸C₅ = 18! / [ ( 18 -5)! * 5! ] = 8568

Total number of ways to select 5 modems from 22 modems = ²²C₅

²²C₅ = 22! / [ ( 22 - 5)! * 5! ] = 26334

P(Accepting shipment) = P(all 5 modems work) = ¹⁸C₅ / ²²C₅

= 8568 / 26334

= 0.3254