The operator of a communal forest decides to fell trees in order to sell them, either to residents or to businesses. It is assumed that:
\begin{itemize}
  \item among the felled trees, $30 \%$ are oaks, $50 \%$ are firs and the others are trees of secondary species (which means they are of lesser value);
  \item $45.9 \%$ of the oaks and $80 \%$ of the firs felled are sold to residents of the commune;
  \item three quarters of the felled trees of secondary species are sold to businesses.
\end{itemize}

Among the felled trees, one is chosen at random. The following events are considered:
\begin{itemize}
  \item C: ``the felled tree is an oak'';
  \item $S$: ``the felled tree is a fir'';
  \item $E$: ``the felled tree is a tree of secondary species'';
  \item $H$: ``the felled tree is sold to a resident of the commune''.
\end{itemize}

\begin{enumerate}
  \item Construct a complete weighted tree representing the situation.
  \item Calculate the probability that the felled tree is an oak sold to a resident of the commune.
  \item Justify that the probability that the felled tree is sold to a resident of the commune is equal to 0.5877.
  \item What is the probability that a felled tree sold to a resident of the commune is a fir? The result will be given rounded to $10^{-3}$.
\end{enumerate}