In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?

Answer 1

prob defective = .05
prob of good = .95

So we want the prob that all are good
= .95^14
= .48776...

prob of at least one is defective
= 1 - .48776..
= appr. .512

The 8000 does not enter the picture, since we have the percentage
if we used it then we could proceed as follow

numbers defective = .05(8000) = 400
number not defective = 7600

prob not at least one of 14 is defective
= 1 - prob of none defective
= 1 - (7600/8000)^14
= .512

Answer 2

How did you get .95

Answer 3

That's the probability of those non-defective. Defective is 0.5 (5%). So 1-0.5=0.95. @Kojo

Answer 4

First one 3/20
Second one 2/19
third one 1/18
3/20*2/19*1/18 = 1/(3*20*19) =1/1140