Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company just manufactured 796 CD's, and 205 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Answer 1

The probability that the first CD in the sample is not defective is 591/796
The probability that the second CD in the sample is not defective is 590/795
The probability that the third CD in the sample is not defective is 589/794
\[P(sample\ has\ 0\ defective\ CDs)=\frac{591\times 590\times\ 589}{796\times 795\times 794}=you\ can\ calculate \]