The company produces $40 \%$ of small-sized footballs and $60 \%$ of standard-sized footballs.\\
It is admitted that $2 \%$ of small-sized footballs and $5 \%$ of standard-sized footballs do not comply with regulations. A football is chosen at random in the company.

Consider the events:\\
$A$ : ``the football is small-sized'',\\
$B$ : ``the football is standard-sized'',\\
$C$ : ``the football complies with regulations'' and $\bar { C }$, the opposite event of C.

\begin{enumerate}
  \item Represent this random experiment using a probability tree.
  \item Calculate the probability that the football is small-sized and complies with regulations.
  \item Show that the probability of event $C$ is equal to 0.962.
  \item The football chosen does not comply with regulations. What is the probability that this football is small-sized? Round the result to $10 ^ { - 3 }$.
\end{enumerate}