Suppose you have just received a shipment of 20 modems....

Name: Suppose you have just received a shipment of 20 modems. Although you don't know this, 3 of the modems are defective. To determine whether you will accept the shipment, you randomly select 4 modems and test them. If all 4 modems work, you accept the shipment. Otherwise, the shipment is rejected. What is the probability of accepting the shipment?
Uploaded: 2021-06-19T14:40:38-08:00
Duration: 2 min 56 s
Channel: Manisha Sarker
Description: Suppose you have just received a shipment of 20 modems. Although you don't know this, 3 of the modems are defective. To determine whether you will accept the shipment, you randomly select 4 modems and test them. If all 4 modems work, you accept the shipment. Otherwise, the shipment is rejected. What is the probability of accepting the shipment?

Suppose you have just received a shipment of 20 modems. Although you don't know this, 3 of the modems are defective. To determine whether you will accept the shipment, you randomly select 4 modems and test them. If all 4 modems work, you accept the shipment. Otherwise, the shipment is rejected. What is the probability of accepting the shipment?

Transcript

00:01 In this problem, we need to determine the probability of accepting a shipment.

00:05 Now, the probability of the event is the number of favorable outcomes divided by the total number of outcomes.

00:12 Now, first of all, let us determine the total number of outcomes.

00:16 Now, in this problem, there are 20 modems, and we randomly select four modems and test them.

00:23 So the total number of outcomes will be the total number of ways that four modems can be selected out of the 20 modems.

00:30 The order does not matter here, so we can use the concept of combination, and the number of ways will be 20c4, and that will be the total number of outcomes.

00:39 Next, we need to determine the number of favorable outcomes.

00:44 Now, it is said that three of the modems are defective, and the shipment is accepted if all the four modems which have been selected work.

00:54 Now, this will mean that the number of favorable outcomes will be the number of ways that four, four working modems can be selected.

01:02 Now since out of 20 modems, three are defective, that means 20 minus 3, which is 17 modems work.

01:10 So we have to find the number of ways four modems can be selected out of these 17 working modems, so that would be 17c4, because once again the order does not matter and hence we do not require the considering of order, so we only need to consider the selection.

01:28 So we will consider combination and not permutation...

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