The challenge with Bayes' illustrations is to simultaneously.show 1) relations 2) ratios. The suggested approach works well. I am suggesting to combine Venn diagrams and Pie charts:
http://oracleaide.wordpress.com/2012/12/26/a-venn-pie/
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I was very impressed with the simplicity of the Venn diagrams. Making a more intuitive explanation of Bayes Theorem than Bonilla's won't be easy, but obviously it's a worthy cause.
A Venn Pie chart is very intuitive and shows ratios better than Venn diagrams: http://oracleaide.wordpress.com/2012/12/26/a-venn-pie/