Colored Balls in Boxes


I got this little problem from Rustan Leino, who got it from Leonardo de Moura.

I solved it and wrote up my solution.


There are three boxes, one containing two black balls, another containing two white balls, and another containing one black and one white ball. You select a ball uniformly randomly from a box selected uniformly randomly and you find you selected a white ball. What is the probability that the other ball in the same box is also white?

Solution     Reveal