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Understanding
Bayes’Theorem
By David Siegel
1 out of 100 people has nose cancer,
a fictional disease
1
A new test is 98% accurate.2
You test positive.3
What is the likelihood 

that you have the disease?
4
Nose
cancer!
Here is the problem:
You test positive.
What is the likelihood 

that you have the disease?
Here is the problem:
Please work out your answer before continuing …
People
who have
the
disease:
1%
A priori:
True
positives:
1% * 98%
False
positives:
2%
False negatives
Test accuracy: 98%
1% * 2%
After testing everyone:
True
positives:
980
False negatives:
Total population:
100,000
20
False
positives:
2,000
It helps to use numbers:
Chance you
have nose
cancer
True positives
=
All positives
Given that you tested positive:
Chance you
have nose
cancer
True positives
=
All positives
This is Bayes’Theorem!
Chance you
have nose
cancer
980
=
980 + 2,000
Plug in the numbers:
Chance you
have nose
cancer
980
=
2,980
= 32.88%
Do the math:
33%!
Chances that you have nose
cancer, given that you tested
positive:
Before test
1%
After test
33%
This is called a Bayesian update:
update
What if your test had
been negative?
What is the chance you
have nose cancer now?
Extra-credit question:
Understanding
Bayes’Theorem
Learn more at www.businessagilityworkshop.com

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Understanding bayes theorem