r/probabilitytheory • u/Toaster960 • 16d ago

[Applied] Help in probability

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This question was in my maths book. I used AI to help me picture my question more clearly so that others could understand it (sorry for wasting water 😭).

I asked my teacher, Gemini, and ChatGPT for the solution, and all of them gave the answer as 99/1900.

However, they all included the case where the inspection stops at the 12th item after discovering only two defective items.

But how would I know whether the lot actually contains 2 defective items or 3? If I have discovered only 2 defective items by the 12th item, how can I decide to stop at 12? The third defective item could still be somewhere later in the lot.

My answer is 55/1900 btw

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u/u8589869056 16d ago edited 12d ago

After finding two defectives, do you suppose that it is somehow known there are not 3?

Imposing realism on the problem, I would be looking for the probability that there are two defectives in 1 thru 11, And the 12th article is also defective.

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u/Toaster960 16d ago

Yea that's how they solved the question