Statistics & Probability
Intermediate

Bayes' Theorem

Updates a probability given new evidence.

Formula

P(A∣B)=P(B∣A)P(A)P(B)P(A|B) = \frac{P(B|A)P(A)}{P(B)}

Variables

P(A)Prior
P(BA)
P(B)Evidence

Example

A test 99% accurate on a 1%-prevalence disease still yields many false positives — Bayes shows a positive means only ~50% chance of illness.

Did You Know?

Bayes' theorem powers spam filters, medical diagnostics, and modern AI — yet it was published only after its author's death.

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