Question

In a collection of 54 components 4 are known to be defective. If we select a sample of 8 components at random and without replacement, what is the probability that there will be 2 defective components in this sample?

Answer 1

There are total 54 components. Out of them 4 are defective. Then number of non defectives are 54-4 = 50.

Now we are selecting 8 samples out of 54. Then all possible case of choosing 8 from 54 without replacement is

Now we want exactly 2 defective. So this 2 defectives can be choosen from 4 defectives in the collection in ways

Then the remaining 6 non defectives can be choosen from 50 non defectives in the collection in ways

So total number of ways to choose exactly 2 defectives is =

So the probability of choosing exactly 2 defectives is = = 0.091636