ThmDex – An index of mathematical definitions, results, and conjectures.
F8996
Formulation 3
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $\text{Measurement}, \text{Hypothesis} \in \mathcal{F}$ are each an D1716: Event in $P$
(ii) \begin{equation} \mathbb{P} (\text{Measurement}), \mathbb{P} (\text{Hypothesis}) > 0 \end{equation}
Then \begin{equation} \mathbb{P}(\text{Hypothesis} \mid \text{Measurement}) \mathbb{P}(\text{Measurement}) = \mathbb{P}(\text{Measurement} \mid \text{Hypothesis}) \mathbb{P}(\text{Hypothesis}) \end{equation}