With one method of a procedure called acceptance sampling

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 ABCD Electronics Company has just manufactured 4000 write-rewrite CDs, and 90 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

4000-90 = 3910   (non-defective)

 

 

P(first not defective) = 3910/4000    if not replaced....

 

then (1 less to choose from and 1 less not defective)

 

P(2nd is not defective given first is not defective) = 3909/3999    if also not replaced...

 

then (a total of 2 less to choose from and 2 less not defective)

 

P(3rd is not defective given (1st AND 2nd not defective)) = 3908/3998   

 

Now just multiply these 3 fractions

 

(3910(3909>)(3908)) / (4000(3999)(3998)) = .9339