Make a prediction first
Imagine a test for a rare claimed ability — say, correctly guessing a hidden card more often than chance. Only 1% of people genuinely have this ability. The test correctly identifies 90% of people who really have it, and only 5% of people without it pass by chance. If someone passes the test, what’s the chance they actually have the ability? Most people guess somewhere around 85–95%. Try it below.
Probability someone who passed the test actually has the ability: 15.38%
What changed and why
Both outputs update live as you change any input — this is closed-form arithmetic (Bayes’ theorem), not a simulation, so there’s nothing to wait for. The natural-frequency table and the percentage view are two representations of the exact same calculation; research on Bayesian reasoning shows people answer this kind of question far more accurately from the frequency table (count of real cases, out of the total who passed) than from the equivalent percentages alone.(Gigerenzer & Hoffrage, 1995)
Why the answer feels too high
With a 1% base rate, a 90% sensitivity, and a 5% false-positive rate, only about 15% of people who pass the test actually have the ability — even though the test sounds quite accurate on paper. The reason is that the 99% of people without the ability generate almost five times as many false alarms (49.5 people) as the 1% with the ability generate correct detections (9 people), because there are so many more of them to begin with. This is the single most common way a “reliable-sounding” test or claim ends up being much weaker evidence than it first appears — see base rates and Bayesian updating for the general principle.
Model assumptions
- The claimed ability is treated as fully present or fully absent — real traits and skills are often continuous, which this simplified model does not capture.
- The test’s error rates are treated as fixed and uniform across everyone; in reality, a test’s accuracy can vary across subgroups or conditions.
- The “population” is a natural-frequency modelling device, not a claim about any specific real, measured group of people.
Reproducibility
Every input combination is reflected directly in the URL, so you can copy the link to share the exact scenario you built. There is no randomness in this interactive — the same inputs always produce the same exact output.
Sources and method
The frequency-format approach used here — presenting “9 out of 58.5” rather than “15.38%” — follows research showing this framing substantially improves accuracy on Bayesian reasoning problems, without requiring the reader to know Bayes’ theorem explicitly.(Gigerenzer & Hoffrage, 1995) See conditional probability for the underlying worked example in plain language.