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Bayes' Theorem

\begin{eqnarray*} \text{c.f.,} \\ & & P(A|B) = \dfrac{P(A \cap B)}{P(B)} \\ & & P(B|A) = \dfrac{P(B \cap A)}{P(A)} \\ \neg{A} \\ \sim{A} \\ \thicksim{A} \\ \end{eqnarray*}