Bayes' Theorem - Educational Content

Bayes' Theorem Visualizer

Understand how to revise predictions based on new data.

The Definition

Bayes' Theorem is a fundamental formula in probability that calculates the updated probability of an event (A) given new evidence (B). It relates the likelihood of the evidence to the prior belief.

P(A|B) =

P(B|A) ⋅ P(A) P(B)

Where:
P(A|B) The updated probability after seeing the evidence. Also called the result. is the Posterior,
P(B|A) The probability of seeing this evidence IF the hypothesis is true. is the Likelihood,
P(A) Your initial belief before seeing any new evidence. is the Prior, and
P(B) The total probability of the evidence occurring, regardless of whether the hypothesis is true or false. is the Evidence.

 Interactive Practice

Memorize the Formula

Try writing the theorem below to commit it to memory.

P(A|B) = [P(B|A) * P(A)] / P(B)