> [!NOTE] Lemma > Let $(\Omega, \mathcal{F}, \mathbb{R})$ be a [[Probability Space|probability space]]. For all $A \in \mathcal{F},$ the [[Probability Measure|probability measure]] $\mathbb{P}$ satisfies $\mathbb{P}(\Omega\setminus A)=1-\mathbb{P}(A),$where $\Omega\setminus A$ is a [[Set Difference|set difference]]. **Proof**: Follows from [[Probability of Subset of Event]] since $\mathbb{P}(\Omega)=1.$