Question

Among 20 metal parts produced in a machine shop, 5 are defective. If a random sample of three of these metal parts is selected, find:

1. The probability that this sample will contain at least two defectives?
2. The probability that this sample will contain at most one defective?

Answer 1

Here it is given that out of 20 metal parts 5 are defective, hence probability of defective is

Now sample is selected with n=3

As we see that n=3 is constant, p=0.25 is same for all, events are independent and only two outcomes, hence all the properties of binomial distribution is satisfied

So we will use binomial distribution to find the required probability