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\fancyhead[LO,LE]{Unit 3 Methods Statistics}
\fancyhead[CO,CE]{Andrew Lorimer}

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  \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}

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