

\begin{slide}
\subsection{\bf Bayes Theorem: Conditional}
\subsection{\bf Probabilities---2) Frequency and}
\subsection{\bf Probability}

\begin{itemize}
\item Then $N_1 + N_2 + N_3 + N_4 = N$.

\item We previously defined $P(S)$ and now we expect
\begin{eqnarray}
P(A) & = & \lim_{N\rightarrow\infty} \frac{N_1 + N_3}{N} \nonumber \\
P(B) & = & \lim_{N\rightarrow\infty} \frac{N_2 + N_3}{N} \nonumber \\
P(A+B) & = & \lim_{N\rightarrow\infty} \frac{N_1 + N_2 + N_3}{N} 
\end{eqnarray}

\item This is the usual relationship of probabilities to frequencies.
\end{itemize}
\end{slide}

