▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Measurable space
▾ Measure space
▾ Probability space
▾ Event
Event odds
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 $\mathbb{P}(E) < 1$.