Pólya's urn is a statistical model which uses the following scheme: there is an urn containing n black balls and m white balls. When a ball is drawn, it is then returned with an additional ball of the same colour.
If there are n black balls and m white balls, what is the probability that k black balls are drawn in succession?
I'd know how to calculate the probability for getting exactly k black balls (not necessarity in succession though) in n trials, but what if I got some before I got the two in succession? How can I model that?
I'm stuck so any help would be greatly appreciated, thanks!