Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : \Omega \to \Xi_X$ and $Y : \Omega \to \Xi_Y$ are each a D202: Random variable on $P$
(ii)	$\{ X \in E \}, \{ Y \in F \} \in \mathcal{F}$ are each an D1716: Event in $P$
(iii)	\begin{equation} \mathbb{P}(Y \in F), \mathbb{P}(Y \in F^{\complement}) > 0 \end{equation}

Then \begin{equation} \mathbb{P}(X \in E) = \mathbb{P}(X \in E \mid Y \in F) \mathbb{P}(Y \in F) + \mathbb{P}(X \in E \mid Y \not\in F) \mathbb{P}(Y \not\in F) \end{equation}