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+\setlength\parindent{0pt} + +\begin{document} + + \title{Statistics} + \author{} + \date{} + \maketitle + + \section{Conditional probability} + + \[ \Pr(A|B) = \frac{\Pr(A \cap B)}{\Pr(B)} \quad \text{where } \Pr(B) \ne 0 \] + + \[ \Pr(A) = \Pr(A|B) \cdot \Pr(B) + \Pr(A|B^{\prime}) \cdot \Pr(B^{\prime}) \tag{law of total probability} \] + + For independent events: + + \begin{itemize} + \item \(\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)\) + \item \(\Pr(A|B) = \Pr(A)\) + \item \(\Pr(B|A) = \Pr(B)\) + \end{itemize} + +\end{document} -- 2.47.1