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11\fancyhead[LO,LE]{Unit 3 Methods Statistics}
12\fancyhead[CO,CE]{Andrew Lorimer}
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16\begin{document}
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18 \title{Statistics}
19 \author{}
20 \date{}
21 \maketitle
22
23 \section{Conditional probability}
24
25 \[ \Pr(A|B) = \frac{\Pr(A \cap B)}{\Pr(B)} \quad \text{where } \Pr(B) \ne 0 \]
26
27 \[ \Pr(A) = \Pr(A|B) \cdot \Pr(B) + \Pr(A|B^{\prime}) \cdot \Pr(B^{\prime}) \tag{law of total probability} \]
28
29 For independent events:
30
31 \begin{itemize}
32 \item \(\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)\)
33 \item \(\Pr(A|B) = \Pr(A)\)
34 \item \(\Pr(B|A) = \Pr(B)\)
35 \end{itemize}
36
37\end{document}