# Bayes' theorem

- Helps you figure out the likelihood of something existing by using evidence to update your guess on the likelihood
- Core tool for machine learning and AI

## Formula

$P(Aâˆ£B)=\frac{P(B|A) \cdot P(A)}{P(B)â€‹}$ - $|$ means "given that"

- $P(A|B)$
- Probability of event A occurring given that B is true
- Posterior probability

- $P(B|A)$
- Probability of event B occurring given that A is true

- $P(A)$
- Probability of event A occurring on its own
- Prior probability -- what you believed before considering new evidence (B)

- $P(B)$
- Probability of event B occurring on its own