Both ponds have red fish and grey fish. One pond has mostly gray fish, and the other has mostly red fish. The fish are otherwise identical. A man is fishing from one of the two ponds, but you don’t know which. How many fish do you want to see him catch before you’re confident about which pond he’s fishing? You don’t get to see the order he catches them in; you pick a number, and when he’s caught that number, you see the count of grey fish and red fish. Spoiler your answer and don’t check others’ answers before you reply.
I'm going to assume that "mostly" represents a significant majority, and not just a 51/49 split, because if the difference were negligible, it wouldn't matter. I'm also going to assume that the fish are evenly distributed in both ponds, and that there is no notable difference between the fish aside from color. (For instance: it isn't the case that red fish swim in shallow water close to shore and gray fish swim only in deep water, which could make red fish dominate the catch even if their overall numbers were fewer.)
If there's unlimited fish in each pond, then I ignore the question, kill the fisherman and set up nets and make out like a fucking king in the seafood market.
This would be basic statistical analysis, except that the key variable - population size - has been omitted. Given that we could work out exactly what observation would be required to establish the answer to an arbitrary degree of accuracy.
0 because fishing is fucking tedious and I don't want to waste all morning waiting for him to catch a statistically significant sample size.
True, but the question as asked simply says "confident." Without knowing more, I couldn't be confident with It's an easy matter of statistics if you know what the ratio is (or what the lower limit of it is). If you know it's 60/40 then you can compute the number of samples that will give you the result with any level of confidence (approaching 100%) that you desire. But the ratio is not given. The problem does not state what the penalty is for being wrong, but if the standard is confidence, then it's irrelevant.
