Probability & Combinatorics
Advanced

Bayes Theorem

Reverses conditional probabilities using prior knowledge.

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

Core of spam filters and medical testing

Did You Know?

Bayes theorem underpins much of modern statistics and machine learning.

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