Hi all, first post, and not entirely sure it belongs here, but the problem seems hard enough to me!

I have a bag containing X red balls and Y blue balls.

Balls are withdrawn one at a time until no balls remain.

What is the expected number of times that two blue balls are withdrawn in a row?

(E.g. in: r b b r b r r b b b b, there are 4 b-b events)

Is it possible to work out a general formula?