The Bayes’ law is very easy to understand when it is explained visually. Venn diagrams are a very popular way to represent relations between sets in the Bayes’ theorem.
Unfortunately, Venn diagrams are inefficient in showing ratios.
The best kind of diagrams to show ratios are the pie charts.
Combining Venn and Pie – by allowing pie sectors to overlap – makes diagrams more descriptive and illustrations of Bayes’ theorem – more intuitive.
We could add some depth and make a 3D diagram to show that sets (or events) intersect.
If we keep realistic proportions between sector sizes (even approximately), then the popular problem about cancer becomes less dreadful.
One day I will complete and publish an applet which makes it easy to play with interactive Venn Pies.
This is done.