From 3661ee2a2d236aa5db193d943ce944db32ddf093 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 4 Jan 2021 14:31:15 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20DS=20pour=20les=20maths=20compl=C3=A9me?= =?UTF-8?q?ntaires?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Complementaire/DS/DS_21_01_07/DS_21_01_07.pdf | Bin 0 -> 52962 bytes Complementaire/DS/DS_21_01_07/DS_21_01_07.tex | 85 ++++++++++++++++++ 2 files changed, 85 insertions(+) create mode 100644 Complementaire/DS/DS_21_01_07/DS_21_01_07.pdf create mode 100644 Complementaire/DS/DS_21_01_07/DS_21_01_07.tex diff --git a/Complementaire/DS/DS_21_01_07/DS_21_01_07.pdf b/Complementaire/DS/DS_21_01_07/DS_21_01_07.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2148454e884773a324de173e78112bc5b1b851b8 GIT binary patch literal 52962 zcmce-bF3&&vo5@B+qP|6d)c;a8++NdZSQ58<+0y{%XC>|atdSwrL69Rg5IYUbmBWEajB^N{I 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Le but de ce jeu est d'affronter des obstacles à l'aide de personnages qui peuvent être de trois types: \og Terre \fg, \og Air\fg{} ou \og Feu \fg. Le jeu a été programmer de telle sorte que chaque partie est indépendante des précédentes. + + Au début de chaque partie, Victor obtient de façon aléatoire un personnage. La probabilité qu'un type \og Terre \fg soit obtenu est de 0.45. + + On considère $3$ parties jouées par Victor, prises indépendamment les unes des autres. $X$ désigne la variable aléatoire qui compte le nombre de personnages de type \og Terre \fg{} obtenus au début de ses $3$ parties. + + \begin{enumerate} + \item Justifier que cette situation peut être modélisée par une loi binomiale dont on précisera les paramètres. + \item Tracer l'arbre de probabilité modélisant cette situation. + \item Calculer la probabilité que Victor ait obtenu exactement 2 personnages de type \og Terre \fg{} au début de ses $3$ parties. + \item Calculer la probabilité que Victor ait obtenu au moins une fois un personnage de type \og Terre \fg. + \item Combien de personnages de type \og Terre \fg{} peut-il espérer avoir en moyenne sur ses 3 parties? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Technique}, points=5, tribe={complementaire}, type={Exercise}, tribe={1}] + Soit $X \sim \mathcal{B}(60; 0.3)$. + \begin{enumerate} + \item Calculer le quantité suivante en détaillant la formule utilisée: $P(X = 25)$. + \item Calculer les quantités suivantes + \[ + P(X \leq 30) \qquad \qquad P(X > 50) + \] + \item Calculer l'espérance et l'écart-type de $X$. + \end{enumerate} +\end{exercise} + +\pagebreak + +\setcounter{exercise}{0} + +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +\begin{exercise}[subtitle={Technique}, points=5, tribe={complementaire}, type={Exercise}, tribe={2}] + Soit $X \sim \mathcal{B}(80; 0.7)$. + \begin{enumerate} + \item Calculer le quantité suivante en détaillant la formule utilisée: $P(X = 25)$. + \item Calculer les quantités suivantes + \[ + P(X \leq 30) \qquad \qquad P(X > 60) + \] + \item Calculer l'espérance et l'écart-type de $X$. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Jeu}, points=5, tribe={complementaire}, type={Exercise}, origin={Une annale du bac ES}, tribe={2}] + Victor a téléchargé un jeu sur son téléphone. Le but de ce jeu est d'affronter des obstacles à l'aide de personnages qui peuvent être de trois types: \og Terre \fg, \og Air\fg{} ou \og Feu \fg. Le jeu a été programmer de telle sorte que chaque partie est indépendante des précédentes. + + Au début de chaque partie, Victor obtient de façon aléatoire un personnage. La probabilité qu'un type \og Terre \fg soit obtenu est de 0.35. + + On considère $3$ parties jouées par Victor, prises indépendamment les unes des autres. $X$ désigne la variable aléatoire qui compte le nombre de personnages de type \og Terre \fg{} obtenus au début de ses $3$ parties. + + \begin{enumerate} + \item Justifier que cette situation peut être modélisée par une loi binomiale dont on précisera les paramètres. + \item Tracer l'arbre de probabilité modélisant cette situation. + \item Calculer la probabilité que Victor ait obtenu exactement 2 personnages de type \og Terre \fg{} au début de ses $3$ parties. + \item Calculer la probabilité que Victor ait obtenu au moins une fois un personnage de type \og Terre \fg. + \item Combien de personnages de type \og Terre \fg{} peut-il espérer avoir en moyenne sur ses 3 parties? + \end{enumerate} +\end{exercise} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: