# [FoRK] Black Belt Bayesian vs. Authority, Fight!

Matt Jensen <mattj at newsblip.com> on Fri Aug 10 11:16:19 PDT 2007

```Quoting Lion Kimbro <lionkimbro at gmail.com>:

>   3. Bayes theorem is trivial.  I understand it.  I can explain
>       it easily, to anyone.

Give the following problem to someone, and do not prime them by

"1% of women at age forty who participate in routine screening have
breast cancer.  80% of women with breast cancer will get positive
mammograms.  9.6% of women without breast cancer will also get
positive mammograms.  A woman in this age group had a positive
mammography in a routine screening.  What is the probability that she
actually has breast cancer?"

Only about 15% of doctors get this right (See Casscells, Schoenberger,
and Graboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and others;
researchers keep repeating the study and doctors keep getting it
wrong.)  Most doctors estimate the probability to be between 70% and
80%. The correct answer is 7.8%.

Maybe you are very good at explaining this to people. However, there's
been tons of research in the last twenty years showing the poor
reasoning, logic, and intuition most people.  This is one example.

Matt Jensen
http://mattjensen.com
Seattle

```