
\begin{slide}
\subsection{\bf Axioms of Probability}
\begin{itemize}
\item{\bf Axiom 1:} To every set $S$ corresponds a non-negative number $P(S)$ 
which is called the probability of the event $X$ belonging to $S$.

\item{\bf Axiom 2:} $P(Y) = 1$

\item{\bf Axiom 3:} $P(S)$ is a completely additive set function:

i.e., $P\left( S_1 + S_2 + \ldots \right) = P\left( S_1 \right) + P\left( S_2 
\right) \ldots  + \ldots$ if the $S_i$ are disjoint.

$S_i S_j = 0$, \hspace{1em} $i\ne j$
\end{itemize}
\end{slide}

