A quality control engineer inspects a random sample of three batteries from each lot of 30 car batteries, which is ready to be shipped.
If such a lot contains ten batteries with slight defects, what then is the probability that the inspector’s sample contain
(a) None of the batteries with slight defects?
(b) At least one of the batteries with slight defects?
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We have the set A of 30 items and its subset B of defective items consisting of 10 items.
We randomly select 3 items from the set A.
If no one of these 3 items is defective, it means that this triple of items is selected from the subset of 20 good items.
The probability to have good item at the first selection is .
The probability to have good item at the second selection (having good item at the first selection) is .
The probability to have good item at the third selection (having good items after the first and second selections) is .
The probability to have good triple is thus the product = = = = 0.280788.
It is the answer to question (a).
The answer to question (b) is the COMPLEMENT 1 - 0.280788 = 0.719212.
Solved.