# Tough (algebraic) probability problem.

1. Jun 27, 2008

### mathwizarddud

How many ordered pairs $$(b,y)$$ of positive integers with $$4 \le b \le y \le 2007$$ are there such that when $$b$$ blue balls and $$y$$ yellow balls are randomnly arranged in a row, the probability that the balls on each end have the same colour is $$1/2$$?

PS: Is there a button such that I could just click on it after I highlighted the text that I want to be included in the LaTeX tags? It's going to save me a lot of typing if there's such button (without keep typing [tex] and so on)!

Last edited: Jun 27, 2008
2. Jun 28, 2008

### matt grime

This just looks like some conditional probability problem. Is it homework, a challenge for the rest of us, or something else?