# Bayes' Theorem

## Main Question or Discussion Point

Dear all,

1.) The difference of conditional probability and Bayes' formula.

2.) Is Bayes' formula a "all weather condition" formula for all conditional probabilities problem?

Thank you,

S

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1) Conditional probability is $$\mathbb{P}(A|B):=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}$$.
$$\mathbb{P}(A|B):=\frac{\mathbb{P}(B|A) \mathbb{P}(A)}{\mathbb{P}(B)}$$
2) You can use Bayes formula for any conditional probabilities such that $$\mathbb{P}(B)>0$$