

\begin{slide}
\subsection{\bf 1.2\hspace{1em}  Bayes Theorem: Conditional}
\subsection{\bf Probabilities---1) Frequency Approach}
\begin{itemize}
\item Take two possible (Borel) subsets of $Y\in \Re_k$.  Call them $A$ and
$B$.

$A$ could be point $x=0$.

$B$ could be point $x=1$ only.

\vspace*{10pt}
\centerline{\psfig{figure=fig2.phys.ps,clip=true,width=4.5in}}
\vspace*{10pt}

\item Generally, $Y$ is divided into four subspaces by $A$ and $B$, and
following the chalk dust method---imagine $N$ experiments, which give
the following number of occurrences $N_i$ for events to fall in the four
subspaces.
\begin{eqnarray*}
N_1 & = & n(A-AB) \\
N_2 & = & n(B-AB) \\
N_3 & = & n(AB) \\
N_4 & = & n\left( (A+B)^* \ \mbox{complement of}\ (A+B)\right)
\end{eqnarray*}
where $n(S)$ is number of events falling in subspace, $S$. 
\end{itemize}
\end{slide}

