\section*{Part A}
Louise drives to work with her car. Her colleague Zoé does not own a car.\\
Each morning, Louise therefore offers to give Zoé a ride. Whatever Zoé's answer, Louise offers to drive her back in the evening.\\
We consider a given day. We have the following information:
\begin{itemize}
  \item the probability that Louise drives Zoé in the morning is 0.55;
  \item if Louise drove Zoé in the morning, the probability that she drives her back in the evening is 0.7;
  \item if Louise did not drive Zoé in the morning, the probability that she drives her back in the evening is 0.24.
\end{itemize}
We denote $M$ and $S$ the following events:
\begin{itemize}
  \item $M$: ``Louise drives Zoé in the morning'';
  \item S: ``Louise drives Zoé back in the evening''.
\end{itemize}
\begin{enumerate}
  \item Construct a probability tree representing the situation.
  \item Calculate $P ( M \cap S )$. Translate this result with a sentence.
  \item Prove that the probability of event S is equal to 0.493.
  \item We know that Louise drove Zoé back in the evening. What is the probability that Louise drove her in the morning?
\end{enumerate}