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 has just manufactured 1651 ​cds, and 539 are defective. if 3 of these cds are randomly selected for​ testing, what is the probability that the entire batch will be​ accepted? does this outcome suggest that the entire batch consists of good​ cds? why or why​ not? whats the sample size

Answer 1

The problem can be solved using hypergeometric distribution, but for relatively simple cases, we can work it out by reasoning.

Given d=539 defectives in a batch n=1651, and the sampling size is 3.
This means that there are 1651-539=1112 good items.

The probability of picking three good items is therefore
P(GGG)=1112/1651 * 1111/1650 * 1110/1649 
=4155544/13612495
=0.30527 (to 5 places of decimal)

Answer: the probability of passing the test is 0.30527 (to 5 decimal places)