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Import work from year 2014-2015

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Benjamin Bertrand
2017-06-16 09:48:07 +03:00
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\documentclass[a4paper,10pt,xcolor=table]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classPres}
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
\author{}
\title{}
\date{}
\begin{document}
\begin{frame}{Goûts et couleurs de chacuns}
Dans un groupe de 20 personnes, il y a
\begin{itemize}
\item 10 personnes qui aiments la pêche
\item 8 qui aiment la lecture
\item 5 qui n'aiment ni la pêche ni la lecture
\end{itemize}
~\\[1cm]
\begin{enumerate}
\item Combien de personnes n'aiment ni la pêche ni la lecture?
\item Combien de personnes uniquement la pêche?
\item Combien de personnes uniquement la lecture?
\item Combien de personnes aiment les deux activités?
\end{enumerate}
\end{frame}
\begin{frame}{Formes et couleurs}
Dans un sac, il y a 50 objets,
\begin{itemize}
\item 30 objets sont ronds
\item 20 objets sont rouges
\item 10 objets sont ronds et rouges
\end{itemize}
On définit les ensembles suivants
\begin{itemize}
\item $A = \left\{\mbox{objet rouge} \right\} $
\item $B = \left\{\mbox{objet rond} \right\} $
\end{itemize}
~\\[0.5cm]
On tire au hasard un objet dans ce sac.
\begin{enumerate}
\item Calculer $P(A)$ puis $P(B)$.
\item Décrire $A\cap B$. Calculer $P(A\cap B)$.
\item Décrire $A\cup B$. Calculer $P(A\cup B)$.
\end{enumerate}
\vfill
\end{frame}
\begin{frame}{Voitures cassées}
Le schéma suivant représente les défauts présent sur un ensemble de 300 voitures. Les effectifs de chaque groupe sont indiqués.
On choisit au hasard une voiture parmi toutes ces voitures.
\begin{minipage}{0.5\textwidth}
On note $M$ et $P$ les événements:
\begin{itemize}
\item $M = \left\{ \mbox{ Le moteur est cassé } \right\}$
\item $P = \left\{ \mbox{ le pneu est crevé } \right\}$
\end{itemize}
\end{minipage}
\begin{minipage}{0.3\textwidth}
\includegraphics[scale=0.2]{fig/patates_proba_2nd}
\end{minipage}
\begin{enumerate}
\item Quelle est la probabilité d'avoir une voiture sans défauts?
\item Décrire (en français) les ensembles suivants
\begin{eqnarray*}
M \cup P \qquad M \cup \bar{P} \qquad M \cap P \qquad \overline{M \cap P}
\end{eqnarray*}
\item Calculer la probabilité de $M$, $P$, $M\cap P$, $M \cup P$.
\item En déduire la probabilité de $\overline{M \cap P}$;
\end{enumerate}
\end{frame}
\end{document}

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2nd/Proba_stat/Proba_Ens/Exo/index.rst Normal file
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Notes sur des exercices mélangeant probabilites et ensembles
############################################################
:date: 2015-07-01
:modified: 2015-07-01
:tags: Proba,Exo
:category: 2nd
:authors: Benjamin Bertrand
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
`Lien vers prop_UI.tex <prop_UI.tex>`_
`Lien vers Union_inter.tex <Union_inter.tex>`_
`Lien vers Union_inter.pdf <Union_inter.pdf>`_
`Lien vers prop_UI.pdf <prop_UI.pdf>`_
`Lien vers fig/patates_proba_2nd.png <fig/patates_proba_2nd.png>`_
`Lien vers fig/patates_proba_2nd_bis.png <fig/patates_proba_2nd_bis.png>`_

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\documentclass{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classConn}
% Title Page
\title{}
\author{}
\date{}
\begin{document}
\begin{multicols}{2}
\textbf{exercice 1:}\\
Soit $\Omega$ l'univers et $A$ et $B$ deux évènements de $\Omega$ tels que $p(A) = 0.5$, $p(B) = 0.6$ et $p(A\cap B) = 0.3$.\\
Calculer $p(\overline{A})$, $p(\overline{B})$ et $p(A\cup B)$.
\textbf{exercice 2:}\\
Soit $\Omega$ l'univers et $A$ et $B$ deux évènements de $\Omega$ tels que $p(A) = 0.7$, $p(B) = 0.3$ et $p(A\cup B) = 0.8$.\\
\begin{enumerate}
\item Calculer $p(\overline{A})$, $p(\overline{B})$ et $p(A\cap B)$.
\item En déduire $p(\overline{A\cap B})$. faire un diagramme pour représenter $\overline{A\cap B}$.
\end{enumerate}
\textbf{exercice 3:}\\
Le schéma suivant représente les défauts présent sur un ensemble de 300 voitures. Les effectifs de chaque groupe sont indiqués.
On choisit au hasard une voiture parmi toutes ces voitures.
On note $M$ et $P$ les événements:
\begin{itemize}
\item $M = \left\{ \mbox{ le moteur est cassé } \right\}$
\item $P = \left\{ \mbox{ le pneu est crevé } \right\}$
\end{itemize}
\begin{center}
\includegraphics[scale=0.3]{fig/patates_proba_2nd}
\end{center}
\begin{enumerate}
\item Quelle est la probabilité d'avoir une voiture sans défauts?
\item Décrire (en français) les ensembles suivants
\begin{eqnarray*}
M \cup P \qquad M \cup \overline{P} \qquad M \cap P \qquad \overline{M \cap P}
\end{eqnarray*}
\item Calculer la probabilité de $M$, $P$, $M\cap P$, $M \cup P$.
\item En déduire la probabilité de $\overline{M \cap P}$;
\end{enumerate}
\columnbreak
\textbf{exercice 1:}\\
Soit $\Omega$ l'univers et $A$ et $B$ deux évènements de $\Omega$ tels que $p(A) = 0.5$, $p(B) = 0.6$ et $p(A\cap B) = 0.3$.\\
Calculer $p(\overline{A})$, $p(\overline{B})$ et $p(A\cup B)$.
\textbf{exercice 2:}\\
Soit $\Omega$ l'univers et $A$ et $B$ deux évènements de $\Omega$ tels que $p(A) = 0.7$, $p(B) = 0.3$ et $p(A\cup B) = 0.8$.\\
\begin{enumerate}
\item Calculer $p(\overline{A})$, $p(\overline{B})$ et $p(A\cap B)$.
\item En déduire $p(\overline{A\cap B})$. faire un diagramme pour représenter $\overline{A\cap B}$.
\end{enumerate}
\textbf{exercice 3:}\\
Le schéma suivant représente les défauts présent sur un ensemble de 300 voitures. Les effectifs de chaque groupe sont indiqués.
On choisit au hasard une voiture parmi toutes ces voitures.
On note $M$ et $P$ les événements:
\begin{itemize}
\item $M = \left\{ \mbox{ le moteur est cassé } \right\}$
\item $P = \left\{ \mbox{ le pneu est crevé } \right\}$
\end{itemize}
\begin{center}
\includegraphics[scale=0.3]{fig/patates_proba_2nd}
\end{center}
\begin{enumerate}
\item Quelle est la probabilité d'avoir une voiture sans défauts?
\item Décrire (en français) les ensembles suivants
\begin{eqnarray*}
M \cup P \qquad M \cup \overline{P} \qquad M \cap P \qquad \overline{M \cap P}
\end{eqnarray*}
\item Calculer la probabilité de $M$, $P$, $M\cap P$, $M \cup P$.
\item En déduire la probabilité de $\overline{M \cap P}$;
\end{enumerate}
\end{multicols}
\end{document}
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