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Suppose I have a box with N marbles of different color and I want to know the ratio of the number of green ones to N (number X). The number of marbles (N) is so huge that there`s absolutely no way to get them all out of the box and count. What I do instead is I take a sample of M randomly picked marbles and count the ratio of green ones within this sample. I obtain another value - Y.

It is obvious that as M approaches N, Y approaches X. The question is: up to what significant figure can I trust the value of Y?

I know that to get a proper answer I have to calculate probabilities of each significant figure being correct and then establish a trust boundary (let`s say, if it is 90% or more - I consider it to be correct). And I do understand the process of calculation. My question is the following:

Is there an already well established solution for this problem that I can just quote in my essay and avoid adding unnecessary information? I`m pretty sure that it exists, since I can`t be the only one facing this problem. I just need the name :)

Deep Thanks!

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# Sampling accuracy estimation

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