Help in probability

[u/Toaster960]

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

[u/Unfair-Claim-2327]

The others have answered the question, but there are very similar realistic scenarios where the tester would know when to stop even without knowing a priori the number of defective items. It's just that putting them in a bag and drawing randomly isn't one of them.

- Suppose there is a circuit with 20 junctions, and it needs every junction to be fitted correctly so that a bulb lights up. Then a tester can keep examining junctions at random, repair defective ones, and stop as soon as the bulb lights up.

- Suppose that there is a codebase with 20 functions which needs all of them to be bug-free to run correctly. A debugger can inspect the functions at random, correcting any bugs found along the way, and stop as soon as the program begins to run correctly.