Pulling balls out of a box A box has $b$ blue balls and $r$ red balls. We pull the balls without returning them. What is the probability that the $k$th pull is the first red ball and what is the probability that the last ball is red?
Also: do you know a site which fully explains these kinds of problems and all the variation you can have?

Answering the first question:
$\left(\prod\limits_{n=0}^{k-2}\dfrac{b-n}{b+r-n}\right)\cdot\left(\dfrac{r}{b+r-(k-1)}\right)$
