This is a very well done presentation - I am genuinely impressed. We could use more of these types of explanations. The more people who understand, the more help we have.
I have always visualized probability and conditional probabilities in terms of Venn diagrams, it is easier to understand stuff this way. I think this is _the_ best way to teach probability to a beginner. What do you think ?!
I think of it as the joint variable event space relative to (or normalized by) the condition variable event space. In a few words what is shown in the article diagrams.
An explanation similar to this was what made Bayes' theorem really click for me when I took probability. Thanks Prof. Terpstra!<p><a href="http://www.ndsu.nodak.edu/ndsu/normann/statistics/faculty/terpstra/index.html" rel="nofollow">http://www.ndsu.nodak.edu/ndsu/normann/statistics/faculty/te...</a>
I don't actually remember the formula for Bayes' theorem. I just visualize it as shown in this article, and write down equations from there. For me, anyway, that is actually a more reliable way of working.
I just skimmed the article, having received treatments of Bayes' theorem many times over the course of my almost-finished college career; however, I think this is neat, because making use of visualization/imagery is a good approach to teaching and understanding statistics, which the human brain is (typically) not capable of handling well.