This is an applet for a blog post
Using Venn Pie Charts to illustrate Bayes' theorem
Here is a classical Bayesian problem
from the famous Yudkowsky's "An Intuitive Explanation of Bayes' Theorem":
1% of women at age forty who participate in routine screening have breast cancer.
80% of women with breast cancer will get positive mammographies.
9.6% of women without breast cancer will also get positive mammographies.
A woman in this age group had a positive mammography in a routine screening.
What is the probability that she actually has breast cancer?
The Venn Pie Chart (I admit - I made up the term) describes events presented in the problem using colored overlapping
The pink sector represents frequency of the first event (A), women having breast cancer.
The gray sector represents frequency of the second event (B), women having a positive test.
The area where sectors overlap (the dark gray sector),
represents frequency of the second event given that the first one has
happened (B|A or "B given A").
Ratios of sector areas (or arcs) represent probabilities of events.
How is it different from Venn diagrams or Pie Charts?
It is different from a regular Pie Chart because its sectors overlap.
It is different from a regular Venn (or, rather, Euler) diagram because it presents sets using sectors, not circles.
Just click the "Draw" button, and observe that:
Percentage of women with breast cancer - the pink sector - is still just 1%.
The most confusing number in the whole problem is 80%.
It is the dark gray sector - representing women with positive test and
cancer. And it covers only part (80% to be precise) of the tiny pink
sector, not the whole circle (a.k.a. universe).
There is a lot of false positives - the light gray sector, covering 9.6% of the white area (not the whole circle!).
Feel free to explore different combinations of probabilities: (50,50,50), (25,25,25), (25,50,25), (30,30,30), (50,0,50).