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\subsection*{Exercise on probability}
Consider the following process  $P$:
\[
a.(b.0 \oplus_{1/2} c.0) + a.(\tau.b.0 + \tau.c.0)
\]
Assume that $a$, $b$ and $c$ are pairwise different. 
$P$ gives rise to the following transition graph:

\vspace{7cm}

\begin{itemize}
\item How may different schedulers we have for $P$? 
\item What is the probability that $b$ will be executed, under the different schedulers?
\end{itemize}
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\subsubsection*{Solution}
\begin{itemize}
\item There are 3 different schedulers:
 \begin{itemize}
 \item The scheduler $\sigma_1$, which selects the transition {\bf I},
 \item  the scheduler $\sigma_2$, which selects the transition {\bf II} and then {\bf III},
\item the scheduler $\sigma_3$, which selects the transition {\bf II} and then {\bf IV}.
\end{itemize}

\item
The probability of performing $b$ is
\begin{itemize}
\item $1/2$ under $\sigma_1$,
\item $1$ under $\sigma_2$, 
\item $0$ under $\sigma_3$.
\end{itemize}
\end{itemize}


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