Are we able to easily give a probability of finding a rare item if said rare items are randomly distributed amongst other items? For example, say that we have a container full of $n$ molecules, and exactly $m$ of those molecules are of type $A$. If we put a random divider in the container so that each side of the divider has $\frac{n}{2}$ molecules, can we determine the probability that each side of the divider also contains exactly $\frac{m}{2}$ $A$ molecules?
Is that just essentially the same as if you individually pick out half of the molecules multiplying all the probabilities of picking out the different types of particles?