This is my favorite explanation of the theorem so far:
http://oscarbonilla.com/2009/05/visualizing-bayes-theorem/
But I doubt you can explain it to middle school students in only 3 min. If I were you, I wouldn't discuss the theorem itself, just the cancer patient problem. Have the students try to figure out the answer for themselves, and then surprise them with the real answer (and justify it by talking about a population of 1 million people or whatever; your explanation doesn't have to use probabilities, although the problem statement could).
Nice one, I like it!
But there's something I fail to understand: where's the 9.6% rendered?
"9.6% of the area outside of event A." - wait, doesn't that little area outside A represent the women with cancer?
Next Monday I am supposed to introduce a bunch of middle school students to Bayes' theorem.
I've scoured the Internet for basic examples where Bayes' theorem is applied. Alas, all explanations I've come cross are, I believe, difficult to grasp for the average middle school student.
So what I am looking for is a straightforward explanation of Bayes' theorem that uses the least amount of Mathematics and words possible. (Also, my presentation has to be under 3 minutes.)
I think that it would be efficient in terms of learning for me to use coins or cards, something tangible to illustrate what I'm talking about.
What do you think? How should I teach 'em Bayes' ways?
PS: I myself am new to Bayesian probability.