With one method of acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defect. An electronics company has just manufactured 2500 CDs, and 2% are defective. If 4 of the CDs are selected and tested, what is the probability that the entire batch will be rejected?
Ok so I know how to set up the formula for this up to a point:
P(reject batch)= P(at least one is defective)
= 1-P (all good)
In the end the professor's answer is P(reject batch)=1-(2450/2500)*(2449/2499)*2448/2498)*(2447/2497)=.0777
But I just don't understand HOW she got 2450 and so on....what did she subtract 2500 from to get that. I also understand why the denominator changed but don't get the numerator part of the final answer.