A machine produces widgets at a defective rate of 9%. A sample of 8 widgets is taken, What is the probability that 3 of them are defective?

Question

A machine produces widgets at a defective rate of 9%. A sample of 8 widgets is taken, What is the probability that 3 of them are defective?

 

Explanations would be most helpful!

Answer 1

This is a binomial probability with p=0.09, as stated in the problem. The event of interest is finding a defective widget, which is given at 9%. So in the context of this problem, a "SUCCESS" is finding a defective widget.

 

We are looking for 3 SUCCESSes in 8 trials.

 

The formula is (N choose k) * p^k * (1-p) ^(N-k)

 

              (8 choose 3)* (0.09)^3 * (0.91)^5 

 

     where 8 choose 3 =   8!/(3!)(8-3)! = 8! / (3!5!) = 8*7*6/6 = 56

 

So 56 * (0.09)^3 * (0.91)^5 0.0254754883 or just over 2.5%