Dear people who write math: Don't write text as-is in math mode. Either use \mathrm/\mathit (for LaTeX) or "" (for Word) to prevent random text being interpreted (and typeset as) variables adjacent to each other. The spacing for $numberOfYellowPegs$ is particularly horrifying.
I think it should be pointed out that bayesian's believe bayes theorem as a statement about plausibility of statements, so intuitions about an event space (which are obvious statements about sets) don't carry over to the general case.
The best reference is Jaynes's Probability Theory: The Logic of Science. The first three chapters are online for free and explain the development of probability theory as a logic for plausible reasoning [1]. If you want to get a quick taste, I wrote a short blog post that introduces the theory while working through an interesting coin-toss problem [2].
Great work! Recently I've been contemplating the idea of starting a blog that explains math concepts using LEGO bricks, this post gave me faith that there will be some interest in such a thing!
That's quite nice; well done. The Lego definitely helps communicate intuition. I also like how you're very thorough in the computations -- it makes a good introduction.
