I'm self-taught in statistics, so I have some holes in my knowledge for sure. please bear with me.

I have a hard time defining my problem. I want to figure out if my selection procedure (governed by hardware) produces a flat, or close enough to flat probability mass function that I can work on the resulting data as if it was uniformly distributed.

from a limited set of data (my sample space $S_A$) I select a random data entity, containing some items, I call this $S_B$. I use random selection for this (uniform), so $P(A)=1/N_A$.

In $S_B$ I select $m$ random items, for $B\choose m$ combinations. In my project I do work on these random items. The catch is that $S_B$ contains some elements that cannot be changed, and the elements that cannot be changed are not distributed evenly. So I believe that $m$ changes.

But maybe the problem can be represented as the intersection of all the probabilities $P\left(A\cap B\cap C^{\prime}\right)$ where $P(A)=1/N_A$, $P(B)=1/{B\choose m}$, and $P(C)$ is the average chance of an element of $S_B$ being "changeable". $P(C^\prime) = 1 - P(C)$

But still, I'm expecting to be corrected here. I do this selection millions of times to build up statistics on the effects of the change, and also correlate the changes with $S_A$

Just to be clear, $S_B$ is a subset of $S_A$. And the probability I believe I need is the probability that a random element has been changed. What I wish for is that this probability is uniform, or close to it over $S_A$.

The problems I see, are that $P(C)$ is a function in $S_A$. So I'm not really confident in this.

Thanks for any input.


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