Suppose that a sample of size n is to be chosen randomly (without replacement) from an urn containing N balls, of which m are white and N-m are black. If we let X denote the number of white balls selected, then the probability of getting exactly i white balls is

P(X=i)=\frac{\binom{m}i\binom{N-m}{n-i}}{\binom{N}{n}}, i=0,1,\ldots, \min(n,m).

The above probability is for a single "replicate".

In statistics, "Repeated measures" involves measuring the same cases (subjects, people, silicon chips, whatever) multiple times.

"Replication" involves running the same study on different subjects but identical conditions.

For a requirement of a process, I have to "replicate" the above same experiment 2 times and hence find the probability.

But the question itself is not clear to me that what probability I have to calculate if the experiment is replicated twice?


By replicating the above experiment twice, does it mean I need to calculate the probability of having exactly 2i white balls from a sample of 2n balls, which is sampled from 2N balls, of which 2m are white and 2(N-m) are black?

Also it seems to me, the probability of getting exactly i white balls is same for each replicate. But what is the definition of the following probability
\big(\frac{\binom{m}i\binom{N-m}{n-i}}{\binom{N}{n}}\big)^2?