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

(i)	$X : \Omega \to \mathbb{R}$ is a D3161: Random real number on $X$

Let $a, b \in \mathbb{R}$ each be a D993: Real number such that

(i)	\begin{equation} a \leq b \end{equation}
(ii)	$(a, b] \subseteq \mathbb{R}$ is a D1278: Right-closed real interval

Then \begin{equation} \mathbb{P}(a < X \leq b) = \mathbb{P}(X \leq b) - \mathbb{P}(X \leq a) \end{equation}