I posted this to /r/math on reddit and got some very interesting insight. (http://www.reddit.com/r/math/comments/ryy5n/interesting_little_probability_question/

I posted this to /r/math on reddit and got some very interesting insight. (http://www.reddit.com/r/math/comments/ryy5n/interesting_little_probability_question/ http://www.reddit.com/r/math/comments/ryy5n/interesting_litt...) It appears that a basic knowledge of stochastic processes is required to actually be able to solve this problem, so it's one of those things that are actually much more complicated than they first appear.