Mammograms and Physician Statistical Illiteracy
“The probability that a woman of age 40 has breast cancer is
about 1%. If she has breast cancer, the probability that she
tests positive on a (first) screening mammogram is 90%.
If she does not have breast cancer, the probability that she
tests positive is 9%. What are the chances that a woman who tests
positive actually has breast cancer? Many doctors who were presented
with this common medical situation got the answer wrong –
wildly wrong…The answer most commonly given by physicians
was 90%.” The real answer: 10%.
–Gerd Gigenrenzer, Calculated Risks: How to Know When Numbers
Deceive You
More examples here:

YOUR TURN:
Do you have a favorite example of the Base Rate Fallacy?
Any other favorite statistical fallacies?
Any cool math at all to share?
Favorite proof perhaps?