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+\begin{definition}{Cardinal} + + Soit $E$ un ensemble. On appelle \textbf{cardinal} (ou effectif) de $E$ le nombre d'éléments de $E$. On note + \[ + \mbox{Card}(E) = \# E + \] + +\end{definition} + \pagebreak \subsection*{Les probabilités} \begin{definition}{Probabilités conditionnelles} - Soit $A$ et $B$ deux ensembles d'un population totale $E$ avec $A$ un ensemble non vide. \begin{itemize} \item Probabilités de l'évènement $A$ \[ - P(A) = \frac{\mbox{Effectif de $A$}}{\mbox{Effectif total}} + P(A) = \frac{\mbox{Effectif de $A$}}{\mbox{Effectif total}} = \frac{\# A}{\# E} \] \item Probabilités de l'évènement $B$ sachant $A$ \[ - P_A(B) = \frac{\mbox{Effectif des éléments qui sont dans $A$ et $B$}}{\mbox{Effectifs des éléments qui sont dans $A$}} + P_A(B) = \frac{\mbox{Effectif des éléments qui sont dans $A$ et $B$}}{\mbox{Effectifs des éléments qui sont dans $A$}} = \frac{\#(A\cap B)}{\# A} \] \begin{center} \includegraphics[ scale=0.6 ]{./fig/condi_A}