Lesson 40 of 48
Bayes' theorem
Updating a belief when the evidence arrives.
The screening problem — an accurate test for a rare condition — is the most useful counter-intuitive result in applied mathematics, and the reason base rates deserve your suspicion in every claim you meet.
Do this
Work the classic screening problem by hand: high sensitivity and specificity, rare condition. Compute the probability that a positive result is a true positive, then simulate 100,000 people and confirm it.
The question that unlocks the next lesson
A 99%-accurate test for a condition affecting 1 in 10,000 comes back positive. Roughly how likely is it real?
- AAbout 99%
- BAbout 1%
- CAbout 50%
- DAbout 90%