Bayes' Theorem

Idea

Bayes' theorem gives a mathematical rule for inverting conditional probabilities, allowing us to find the probability of a cause given its effect.

Theorem

The theorem is stated mathematically as the following equation:

$$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$

And can be simply proven from the definition of conditional probability:

$$P(A|B)=\frac{P(A\cap B)}{P(B)},P(B|A)=\frac{P(A\cap B)}{P(A)}$$

See also

Bayes' rule