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. The ABC Electronics Company has just manufactured 1950 write-rewrite CDs, and 120 are defective. If 4 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Answer 1

0.7755

Explanation:

If 120 CDs are defective, the number of non-defective CDs in the batch is:

`n=1950-120\\n=1830`

In order for the batch to be accepted, all of the 4 CDs in the sample must not be defective, the probability of that happening is:

`P=(1830)/(1950)*(1829)/(1949) *(1828)/(1948) *(1827)/(1947)\\P=0.7755`

The probability that the entire batch will be accepted is 0.7755.