In France, the consumption of organic products has been growing for several years.

In 2017, the country had $52\%$ women. That same year, $92\%$ of French people had already consumed organic products. Furthermore, among consumers of organic products, $55\%$ were women.

We randomly choose a person from the file of French people in 2017. We denote:
\begin{itemize}
  \item $F$ the event ``the chosen person is a woman'';
  \item $H$ the event ``the chosen person is a man'';
  \item $B$ the event ``the chosen person has already consumed organic products''.
\end{itemize}

\begin{enumerate}
  \item Translate the numerical data from the statement using events $F$ and $B$.
  \item a. Show that $P(F \cap B) = 0{,}506$.\\
  b. Deduce the probability that a person consumed organic products in 2017, given that they are a woman.
  \item Calculate $P_H(\bar{B})$. Interpret this result in the context of the exercise.
\end{enumerate}