Suppose you have just received a shipment of 23 modems. Although you don't know this, 3 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?

5/23

Step-by-step explanation:

The probability of accepting shpment will be 5 out 23 since 5 modems are selected

Therefore

5/23

The probability of accepting the shipment is 0.46 or 816/1771

Step-by-step explanation:

Firstly, it is important that the two categories of modems ai spelt out. That is the number of the good and the defective ones.

since there are 3 defective modems in the entire package (without your knowledge though) sent to you and there are 23 modems therein altogether, then the number of modems in good working condition will be obtained from subtracting the number of the defective modems from the entire pack of 23 modems:

= 23 - 3 = 20 good modems.

There are 20 modems in good condition in the shipment.

Now, the probability of selecting a defective modems is :

The number of defective modems/total number of modems

= 3/23

Again, the probability of selecting a good modem is:

The number of good modem/total number of modem

= 20/23

Since five modems must be tested and confirmed to be in good working conditions before the shipment will be accepted, we will solve to find the probability of picking up 5 good modems without replacement. The result is consequently the probability of accepting the shipment.

Probability of picking up 5 good modems out of the 5 that will be picked without replacement:

= (20/23)×(19/22)×(18/21)×(17/20)×(16/19)

= 1860480/4037880

= 816/1771 or 0.46

The probability of accepting the shipment is therefore, 0.46 or 816/1771