Bayes' theorem calculator
Bayes' theorem turns a test result into the chance it is right, and that chance depends on how common the condition is. When a condition is rare, even an accurate test flags more healthy people than sick ones, so most positives can be false. Counting whole people makes it plain.
Predict first
1 in 100 people have a condition. A test catches 90% of them and wrongly flags 5% of everyone else. You test positive. What are the chances you have it?
Worked example
A screening test catches 99% of cases and wrongly flags 2% of healthy people. One person in 500 has the condition. You test positive.
- Picture 10,000 people: 20 have the condition, and the test flags 20 of them.
- Of the 9,980 who don't, 2% are flagged anyway: 200 people.
- That's 220 positives, and only 20 of them are real.
A positive result is right about 9% of the time. The test is accurate; the condition is rare.
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