The hidden denominator
Imagine a test that is 95% accurate. That sounds decisive. But if the condition is rare, many positive results can still be false positives. The missing ingredient is prevalence: how common the thing was before the test result arrived.
Why intuition struggles
Humans tend to focus on the dramatic new information: the positive test, the alert, the flagged transaction. Bayes' rule asks us to combine that new information with what was already likely.
A better question
Do not ask, “How accurate is the test?” Ask, “Out of 10,000 people like this, how many would truly have the condition, and how many would be false alarms?” Counts often make the answer clearer than percentages.