What does it mean to "condition on the margin of ____"? I lack statistical/mathematical training and phrases like these leave me bewildered and unsure where to look.
In this post (Which are differences between the hypergeometric distribution and chi-square distribution), there is an example where @Glen_b uses the phrase:
That is, your example data are like so:
Drawn Not drawn Total Red 160 6520 6680 Black 222 11938 12160 Total 382 18458 18840
Looking at the number of reds drawn as a random variable, that has a hypergeometric distribution (though there formulated in terms of white and black balls drawn from an urn rather than red and black balls drawn from a universe).
[Conditioning on the margins gives the hypergeometric - this is also the situation used for Fisher's exact test based on the hypergeometric, and one of the situations for which the usual 2x2 chi-square test of association/test of independence applies. If you don't condition on both margins, you don't have a hypergeometric; but that's what you normally do in the specific balls-in-urns model you describe.]