For me, the most intuitive way of illustrating Bayes' theorem is using Venn diagrams: <a href="http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/" rel="nofollow">http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theor...</a>
This post makes me wish I had access to the web when I went to school. I would probably have launched a collaborative lets-explain-the-math-book-together site or something. Or maybe I would just have played World of Warcraft all day long.<p>What would you have done (or: what did you do if you're not an old f*rt such as me) if you went to school today, with all the technology available?<p>EDIT: I'm 34, by the way. Not _that_ old. :)
I wish authors of these sorts of articles put the correct solution <i>first</i> instead of the incorrect one. I'm more likely to remember the first proof I read and this sort of thing screws me up.<p>Other than that, I found it a really interesting read.
I will confess: I never memorized Bayes theorem. I just imagine rectangles getting chopped into overlapping pieces, and visually derive it every time I need to use it. I've found that this actually worked better for me than trying to apply a formula, since you're less likely to forget intuitions when you're thinking through a problem.<p>Pictures are, by far, my favorite way to explain Bayes theorem.
Monty Hall problem explained wrong. There is no "probability" of Monty opening any "goat door". Monty KNOWS which doors contain goats,and always opens one of them. You have a better chance choosing the remaining door Monty "owns" because he had a 2-out-of-three chance to begin with (you chose randomly and uniformly). He still has that chance. No information was added when he opened a door, because he can ALWAYS open a goat door.