Theorem (Bayes' theorem).

$$ \href{/edifice/probability_measure}{P}(\href{/edifice/set}{A} \href{conditional_probability}{\mid} \href{/edifice/set}{B}) = \frac{\href{/edifice/conditional_probability}{P}(\href{/edifice/set}{B} \href{conditional_probability}{\mid} \href{/edifice/set}{A}) \cdot \href{/edifice/probability_measure}{P}(\href{/edifice/set}{A})} {\href{/edifice/probability_measure}{P}(\href{/edifice/set}{B})} $$