ThmDex – An index of mathematical definitions, results, and conjectures.

Formulation F11034 on D3439: Event odds

F11034

Formulation 0

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)	\begin{equation} \mathbb{P}(E^{\complement}) > 0 \end{equation}

The odds of $E$ in $P$ is the D993: Real number \begin{equation} \frac{\mathbb{P}(E)}{\mathbb{P}(E^{\complement})} \end{equation}

▶▶▶	Comment 0 Result R3719: Probability of complement event shows that $\mathbb{P}(E^{\complement}) = 1 - \mathbb{P}(E)$. Thus, an equvalent assumption to (ii) is that $\mathbb{P}(E) < 1$.