Math Says Yes
Concept

Base Rates

The background frequency of something before you consider new evidence. A strong signal can still produce many false alarms when the thing being tested for is rare, because there are many more non-cases than cases. Good reasoning combines the new signal with the base rate.

Lessons

A huge field of common dots with only a few rare dots under a magnifier.
Rare Things Stay Rare
Even strong evidence can mislead when the thing you are testing for is very uncommon.

Related Facts

Risk & Decisions
4 min · medium
A magnifier over one figure in a crowd, with a few other matching figures faintly marked.
A one-in-a-million match is not a one-in-a-million chance of innocence
When a forensic trait matches 1 in a million people, a big enough population still holds many innocent matches — the match probability is not the probability of innocence.
Risk & Decisions
4 min · medium
A magnifier over a large crowd where only a few figures are coral, the rest teal.
A good test can still scare too many people
When a condition is rare, most positive test results can still be false positives.
Risk & Decisions
5 min · medium
Two tiny dots almost the same size, shown as two very different-height bars through a magnifying glass.
Relative risk vs absolute risk: the difference that changes decisions
Relative risk tells you how many times bigger a risk became. Absolute risk tells you how many extra people are affected.

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