00:01
For this question, we are told that a manufacturer receives a shipment of 100 units, eight of which are defective.
00:09
To determine whether the shipment is rejected or accepted, the manufacturer tests two of the units.
00:18
And so we are asked to construct the probability distribution for the number of defective units in the sample of two.
00:26
So we know we have eight defective units out of 100.
00:31
That means that we have 92 good ones.
00:43
Now the probability of zero defective units in the sample of 2 is the number of ways to select 2 that are good divided by the total number of ways to select 2 from the shipment.
01:11
And so this is 92 choose 2 divided by 100 choose 2.
01:22
We need to select 2 from the 92 good ones in order to have zero defective ones.
01:30
So the number of ways to do that is 92 choose 2.
01:34
And the total number of ways to select 2 from the shipment of 100 is 100 choose 2.
01:41
So this is 4 ,186 divided by 4 ,950, or approximately 0 .847...