Feat(1ST): bilan sur les probas conditionnelles

1ST/08_Probabilite_Conditionnelles/1B_card_ens.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+
+\title{Probabilité conditionnelles - Cours}
+\tribe{1ST}
+\date{Avril 2023}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\section{Ensembles}
+
+\begin{propriete}[Opération d'ensembles]
+   Soit $E$ un ensemble et $A$ et $B$ deux sous ensembles de $E$
+   \begin{center}
+       \includegraphics[scale=1]{./fig/ensembles}
+   \end{center}
+   \begin{multicols}{3}
+       \begin{itemize}[align=right,itemindent=2em,labelsep=2pt,labelwidth=1em,leftmargin=0pt,nosep]
+           \item \textbf{Complémentaire de $A$} contient tous les éléments qui n'ont pas les caractéristiques de $A$.
+
+               \begin{center}
+                   \includegraphics[ scale=0.5 ]{./fig/Abar}
+               \end{center}
+
+           \item \textbf{Intersection de $A$ et $B$} contient tous les éléments qui ont les caractéristiques de $A$ \textbf{ET} de $B$.
+
+               \begin{center}
+                   \includegraphics[ scale=0.5 ]{./fig/inter}
+               \end{center}
+
+           \item \textbf{Union de $A$ et $B$} contient tous les éléments qui ont les caractéristiques de $A$ \textbf{OU} de $B$.
+
+               \begin{center}
+                   \includegraphics[ scale=0.5 ]{./fig/union}
+               \end{center}
+       \end{itemize}
+   \end{multicols}
+\end{propriete}
+
+\begin{definition}[ Cardinal/Effectif]
+    Soit $E$ un ensemble le nombre d'éléments de $E$ est appelé \textbf{effectif} ou \textbf{cardinal} de $E$ et on note
+    \[
+        \mbox{Card}(E) = \#E
+    \]
+\end{definition}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "master"
+%%% End:

1ST/08_Probabilite_Conditionnelles/2B_proba_conditionnel.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+
+\title{Probabilité conditionnelles - Cours}
+\tribe{1ST}
+\date{Avril 2023}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\section{Probabilité conditionnelle}
+
+\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 $A$
+            \[
+            P(A) = \frac{\mbox{Card}(A)}{\mbox{Card}(E)} = \frac{\mbox{Effectif de $A$}}{\mbox{Effectif total}}
+            \]
+        \item Probabilités de l'évènement $B$ sachant $A$
+            \[
+                P_A(B) = \frac{\mbox{Card}(A\cap B)}{\mbox{Card}(A)} = \frac{\mbox{Effectif des éléments qui sont dans $A$ et $B$}}{\mbox{Effectifs des éléments qui sont dans $A$}}
+            \]
+            \begin{center}
+                \includegraphics[ scale=0.6 ]{./fig/condi_A}
+            \end{center}
+    \end{itemize}
+\end{definition}
+
+\paragraph{Exemple}~\\
+
+\begin{minipage}{0.5\linewidth}
+    \begin{tabular}{|*{4}{c|}}
+        \hline
+         & Homme & Femme & Total \\
+        \hline
+        Employé & 10 & 15 & 25 \\
+        \hline
+        Vacataire & 14 & 17 & 31 \\
+        \hline
+        Total & 24 & 32 & 56 \\
+        \hline
+    \end{tabular}
+\end{minipage}
+\begin{minipage}{0.5\linewidth}
+    On note
+    \[
+        A = \left\{ \mbox{Homme} \right\} \qquad
+    \]
+    \[
+        B = \left\{ \mbox{Employé} \right\} \qquad
+    \]
+\end{minipage}
+
+\bigskip
+On choisit au hasard une personne de cette entreprise.
+\begin{itemize}
+    \item
+        \[
+            P(A) =
+        \]
+        Interprétation:
+
+    \item
+        \[
+            P_A(B) =
+        \]
+        Interprétation:
+        \bigskip
+\end{itemize}
+
+\afaire{}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "master"
+%%% End:

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