# Having trouble w/ understanding pdf

1. Oct 26, 2004

### semidevil

so I"m trying to understand pdf, the one where the formula is ((rCk) * (wCn-k))/(NCn). Here, xCx means x chooses x.

anyways, N is the total, and n is how much you sample out of it. and we know that r + w = N.

what is k?

I know this is diffenrent for all problems, but is there an analogy..I"m having trouble setting things up.

2. Oct 26, 2004

### AKG

When you say, "the formula is ..." doesn't it strike you as odd that there is no "=" sign. What is a formula without that sign? What you have is an expression for the probability of getting k of the things which there are r of in total. If "r" represents the number of red balls in total, and "w" represents the number of white balls, then:

$$P(k) = \frac{{r\choose k} {w\choose {n - k}}}{{N\choose n}}$$

However, this only holds for max{0, n – w} ≤ k ≤ min{n, r}. Clearly, the probability is zero otherwise.