Bayes Theorem

$P(H|E)=\frac{P(H)\cdot P(E|H)}{P(E)}$

When to Use

1. You have a hypothesis $P(H)\cdot P(E|H)$
2. You’ve observed some evidence $P(E)$
3. You want: $P(\frac{\text{Hypothesis}}{\text{given the evidence}})$ aka $P(H|E)$

Proof

$P(H|E)$ = $P(E|H)$