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Probabilites - Cours} +\date{2021-11-01} + +\DeclareExerciseCollection[step=2]{banque} +\xsimsetup{ + collect, +} + +\pagestyle{empty} + +\begin{document} + +\input{exercises.tex} +\setcounter{exercise}{1} + +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill + +\end{document} diff --git a/2nd/05_Introduction_Probabilites/exercises.tex b/2nd/05_Introduction_Probabilites/exercises.tex index 6caee9f..f1355e7 100644 --- a/2nd/05_Introduction_Probabilites/exercises.tex +++ b/2nd/05_Introduction_Probabilites/exercises.tex @@ -44,5 +44,46 @@ Jean conclu avec "On va faire le jeu de l'autoroute? C'est moins risqué que d'allumer sont ordinateur ou que d'avoir un accident puis d'être gravement blessé..." Êtes vous d'accord avec leurs propos? - +\end{exercise} + +\begin{exercise}[subtitle={Étranges poissons}, step={2}, origin={Ma tête}, topics={ Introduction Probabilités }, tags={ Probabilité }] + La tableau suivant indique les quantités de poissons d'un étang ayant certaines caractéristiques. + + \begin{center} + \begin{tabular}{|*{5}{c|}} + \hline + & nageoires & ailerons & pattes & total \\ + \hline + bleu & 54 & 10 & 30 & 94 \\ + \hline + vert & 20 & 50 & 34 & 104 \\ + \hline + total & 74 & 60 & 64 & 198 \\ + \hline + \end{tabular} + \end{center} + + Les poissons de cet étang ont été affamé et se jetteront avec la même vigueur sur les appâts de votre canne à pèche. Vous vous préparez pour une bonne partie de pèche. + + \begin{enumerate} + \item Décrire l'expérience aléatoire à laquelle vous vous apprêtez à participer. Préciser l'univers, les issues et expliquer pourquoi on peut modéliser cette situation avec un loi équiprobable. + \item Donner la probabilité des événements suivant arrondis à $10^{-1}$ près. + \begin{itemize} + \item $A = \left\{ \mbox{ le poisson est bleu } \right\} $ + \item $B = \left\{ \mbox{ le poisson a des pattes } \right\} $ + \item $C = \left\{ \mbox{ le poisson a des ailerons vert } \right\} $ + \item $D = \left\{ \mbox{ le poisson est rouge } \right\} $ + \end{itemize} + \item Si on pêche uniquement les poissons à nageoires, quelle est la probabilité d'attraper un poisson vert? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={La pièce}, step={2}, origin={Ma tête}, topics={ Introduction Probabilités }, tags={ Probabilité }] + On prend un pièce de monnaie que l'on considère équilibrée. La face avec la valeur sera notée $N$ et celle avec le dessin $D$. On lance la pièce trois fois de suite et on note les résultats obtenus. + \begin{enumerate} + \item Décrire l'univers et les issues de cette expérience aléatoire. + \item Calculer la probabilité d'avoir le mot $DND$. + \item Est-ce que cette expérience aléatoire peut être modélisée avec une loi probabilité équiprobable. + \item Proposer une variate de cette expérience qui ne l'est pas. + \end{enumerate} \end{exercise} diff --git a/2nd/05_Introduction_Probabilites/index.rst b/2nd/05_Introduction_Probabilites/index.rst index 4726ca1..fcb1a70 100644 --- a/2nd/05_Introduction_Probabilites/index.rst +++ b/2nd/05_Introduction_Probabilites/index.rst @@ -31,6 +31,11 @@ Bilan: Vocabulaire sur la loi de probabilités Situation et tableau de fréquences. +.. image:: ./2E_banque.pdf + :height: 200px + :alt: Quelques exercices classisques + + Bilan: Vocabulaire autour des évènements Étape 3: Lancé de deux dés