00:01
In this problem, we are going to use the concept of combination in order to determine the probability of a certain event.
00:08
Now, in this problem, there is a shipment of 120 electronic components in which four of them are defective.
00:17
Now, in order to determine whether the shipment should be accepted, the engineer randomly selects four of the components and tests them, and the shipment is rejected if one or more of the components is defective.
00:28
Now what we need to determine is the probability that the shipment is rejected.
00:33
Now the probability that the shipment is rejected, that is p of r, can be written as 1 minus p of r bar where r bar denotes the complementary event of r.
00:47
So if p of r is the probability that the shipment gets rejected, then r bar indicates that the shipment is not rejected, that is the shipment is accepted.
00:57
So we will write this as 1 minus the total number of favorable outcomes divided by the total number of outcomes.
01:05
Now the total number of outcomes is the number of ways that four components can be randomly selected out of the total of 120 electronic components.
01:14
Now the order does not matter in this case, so we use the concept of combination and the number of ways in which four components can be selected out of 120 is equal to 120 c4.
01:25
Now the total number of favorable outcomes in this case is the total number of ways in which the shipment can be accepted...