Bayes' theorem as belief updating
Bayes' theorem computes a revised (posterior) probability by combining a prior belief with new evidence via the likelihood. It gives a mechanical rule for how much a new observation should shift your confidence.
Bayes Theorem Examples: A Visual Guide For Beginners
3 ideas
Base rates dominate rare-event tests
The examples show that even an accurate test yields many false positives when the underlying condition is rare, because the small prior swamps the evidence. Ignoring base rates is the classic probability error the book targets.
Learn through worked visual examples
The guide teaches by walking numeric cases and diagrams rather than proofs, building intuition before formalism. Seeing the theorem operate on concrete numbers is the pedagogical method.