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

(i) | $E \in \mathcal{F}$ is an D1716: Event in $P$ |

(ii) | $I_E : \Omega \to \{ 0, 1 \}$ is the D41: Indicator function on $\Omega$ with respect to $E$ |

Then
\begin{equation}
\mathbb{E}(I_E) = \mathbb{P}(E)
\end{equation}