If 4 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

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 1650 write-rewrite CDs, and 70 are defective. If 4 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?

Rounded to four decimal place accuracy.

Answer 1

To calculate the probability we need two numbers, a numerator and a denominator:

First, let's get the denominator, which is the total number of possible outcomes. We are going to choose 4 CD's from a group of 1650. This is found by the combination function C(1650,4)

Next, let's get the numerator, which is the total number of desired outcomes. We want to choose 4 from the non-defective CD's which is 1580. This is found by the combination function C(1580,4)

P = C(1580,4) / C(1650,4) ≈ .8407

If it is not clear why the combination function gives the right numbers, it would probably be worth while to book a lesson.