Feat(1ST): bilan sur les probas conditionnelles
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Probabilité conditionnelles - Cours}
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\tribe{1ST}
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\date{Avril 2023}
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\pagestyle{empty}
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\begin{document}
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\section{Ensembles}
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\begin{propriete}[Opération d'ensembles]
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Soit $E$ un ensemble et $A$ et $B$ deux sous ensembles de $E$
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\begin{center}
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\includegraphics[scale=1]{./fig/ensembles}
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\end{center}
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\begin{multicols}{3}
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\begin{itemize}[align=right,itemindent=2em,labelsep=2pt,labelwidth=1em,leftmargin=0pt,nosep]
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\item \textbf{Complémentaire de $A$} contient tous les éléments qui n'ont pas les caractéristiques de $A$.
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\begin{center}
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\includegraphics[ scale=0.5 ]{./fig/Abar}
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\end{center}
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\item \textbf{Intersection de $A$ et $B$} contient tous les éléments qui ont les caractéristiques de $A$ \textbf{ET} de $B$.
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\begin{center}
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\includegraphics[ scale=0.5 ]{./fig/inter}
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\end{center}
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\item \textbf{Union de $A$ et $B$} contient tous les éléments qui ont les caractéristiques de $A$ \textbf{OU} de $B$.
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\begin{center}
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\includegraphics[ scale=0.5 ]{./fig/union}
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\end{center}
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\end{itemize}
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\end{multicols}
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\end{propriete}
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\begin{definition}[ Cardinal/Effectif]
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Soit $E$ un ensemble le nombre d'éléments de $E$ est appelé \textbf{effectif} ou \textbf{cardinal} de $E$ et on note
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\[
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\mbox{Card}(E) = \#E
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\]
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\end{definition}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Probabilité conditionnelles - Cours}
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\tribe{1ST}
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\date{Avril 2023}
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\pagestyle{empty}
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\begin{document}
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\section{Probabilité conditionnelle}
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\begin{definition}[ Probabilités conditionnelles ]
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Soit $A$ et $B$ deux ensembles d'un population totale $E$ avec $A$ un ensemble non vide.
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\begin{itemize}
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\item Probabilités de l'évènement $A$
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\[
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P(A) = \frac{\mbox{Card}(A)}{\mbox{Card}(E)} = \frac{\mbox{Effectif de $A$}}{\mbox{Effectif total}}
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\]
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\item Probabilités de l'évènement $B$ sachant $A$
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\[
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P_A(B) = \frac{\mbox{Card}(A\cap B)}{\mbox{Card}(A)} = \frac{\mbox{Effectif des éléments qui sont dans $A$ et $B$}}{\mbox{Effectifs des éléments qui sont dans $A$}}
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\]
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\begin{center}
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\includegraphics[ scale=0.6 ]{./fig/condi_A}
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\end{center}
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\end{itemize}
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\end{definition}
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\paragraph{Exemple}~\\
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\begin{minipage}{0.5\linewidth}
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\begin{tabular}{|*{4}{c|}}
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\hline
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& Homme & Femme & Total \\
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\hline
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Employé & 10 & 15 & 25 \\
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\hline
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Vacataire & 14 & 17 & 31 \\
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\hline
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Total & 24 & 32 & 56 \\
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\hline
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\end{tabular}
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\end{minipage}
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\begin{minipage}{0.5\linewidth}
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On note
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\[
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A = \left\{ \mbox{Homme} \right\} \qquad
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\]
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\[
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B = \left\{ \mbox{Employé} \right\} \qquad
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\]
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\end{minipage}
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\bigskip
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On choisit au hasard une personne de cette entreprise.
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\begin{itemize}
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\item
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\[
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P(A) =
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\]
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Interprétation:
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\item
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\[
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P_A(B) =
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\]
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Interprétation:
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\bigskip
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\end{itemize}
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\afaire{}
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\end{document}
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%%% End:
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Reference in New Issue