Please WRITE CLEAR and explain each step Gears produced by a

Please WRITE CLEAR and explain each step.

Gears produced by a grinding process are categorized either as conforming (suitable for in tended purpose), degraded (unsuitable for intended purpose, but usable for other purposes), or scrap (not usable). Suppose that 80% of the gears produced are conforming, 15% are degraded, and 5% are scrap. Ten gears were selected at random. What is the probability that five of them were scrap?

Solution

Given X follows Binomial distribution with n=10 and p=0.05

P(X=x)=10Cx*(0.05^x)*(0.95^(10-x))

So the probability that five of them were scrap is

P(X=5) =10C5*(0.05^5)*(0.95^(10-5)) =0.000060935