A 99% accurate test says you're positive. So you're 99% likely sick, right? Wrong. Here's the base-rate trap in Bayes' theorem, shown by counting 10,000 people.
Hook
99% Accurate. Positive.
Your test is ninety-nine percent accurate, and it says positive. Are you ninety-nine percent sick? No.
- Test is 99% accurate
- Result: positive
- Are you 99% sick?
Setup
10,000 People
Say a disease affects one percent of people. Take ten thousand people and line them up.
- Disease rate: 1%
- Population: 10,000
Count the sick
Sick vs Healthy
One percent is sick. That's one hundred people. The other nine thousand nine hundred are healthy.
- Sick: 100
- Healthy: 9,900
True positives
True Positives: 99
The test catches ninety-nine percent of the sick. That's ninety-nine true positives.
- 99% of 100 sick
- = 99 caught
False positives
False Positives: 99
But it also wrongly flags one percent of the healthy. That's ninety-nine false alarms.
- 1% of 9,900
- = 99 false alarms
Reveal
Everyone Who Tested Positive
Now everyone who tested positive stands together. Ninety-nine sick, ninety-nine healthy.
- 99 truly sick
- 99 healthy
Formula
The Real Probability
So the real chance you're sick is ninety-nine out of one hundred ninety-eight. About fifty percent.
- 99 / 198
- About 50%
Payoff
Don't Ignore the Base Rate
The trap is ignoring the base rate. Rare things stay rare, even after a test. Follow for more math that sticks.
- Rare stays rare
- Follow for more