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 ABCD Electronics Company has just manufactured 6500 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

ABCD Electronics Company manufactured 6500 write-rewrite CDs, and 120 are defective. Since 120 are defective, the number of write-rewrite CDs that would be accepted is (6500 - 120 = 6380).

Since the items at selected without replacement, the number of write-rewrite CDs will continue to decrease anytime a write-rewrite CDs is taken out. For example if they are 6380 accepted write-rewrite CDs if one is taken out they would then be 6379 accepted write-rewrite CDs, and if another one is taken out they would be 6378 accepted write-rewrite CDs and so on.

If 4 of these CDs are randomly selected for testing without replacement,

The probability that the entire batch will be accepted = (6380/6500) × (6379/6500) × (6378/6500) × (6377/6500)

= 0.9815 × 0.9814 × 0.9812 × 0.9811 = 0.9273

The probability that the entire batch will be accepted is 0.9273