Eric Nicholas K's answer to Xiang Ning's Junior College 2 H2 Maths Singapore question.

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Eric Nicholas K
Eric Nicholas K's answer
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Of course, given such a high rate of defective items (at 20%), it is highly unlikely that the batch will be accepted. The first sample of 20 items are very stringent (since more than 2 defective leads to instant rejection) and the next sample of 10 items are even more stringent (none or rejection).

Obviously we do such sample testing (with a small probability of accepting the highly defective batch) as a whole because we can't test each item one by one.

Imagine testing a batch of apples for the quality. If we test EVERY SINGLE apple, then there is no more apple for us to consume! As such, we can only rely on such sample testing of batches to make estimates (albeit with good likelihood) and consequently make the relevant judgement (acceptance or rejection).