From db9ca9c026bdfbbf5db87793deca1f3a48ed21a0 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Wed, 20 Jan 2021 08:57:42 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20d=C3=A9but=20du=20chapitre=20sur=20la?= =?UTF-8?q?=20loi=20binomiale?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/08_Loi_binomiale/1B_definition.pdf | Bin 0 -> 50128 bytes TST/08_Loi_binomiale/1B_definition.tex | 57 +++++++++++++++++++++++++ TST/08_Loi_binomiale/1E_arbres.pdf | Bin 0 -> 23177 bytes TST/08_Loi_binomiale/1E_arbres.tex | 28 ++++++++++++ TST/08_Loi_binomiale/exercises.tex | 19 +++++++++ TST/08_Loi_binomiale/index.rst | 34 +++++++++++++++ 6 files changed, 138 insertions(+) create mode 100644 TST/08_Loi_binomiale/1B_definition.pdf create mode 100644 TST/08_Loi_binomiale/1B_definition.tex create mode 100644 TST/08_Loi_binomiale/1E_arbres.pdf create mode 100644 TST/08_Loi_binomiale/1E_arbres.tex create mode 100644 TST/08_Loi_binomiale/exercises.tex create 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+\geometry{left=10mm,right=10mm, top=5mm, bottom=10mm} + + +\pagestyle{empty} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill +\printcollection{banque} + +\end{document} diff --git a/TST/08_Loi_binomiale/exercises.tex b/TST/08_Loi_binomiale/exercises.tex new file mode 100644 index 0000000..0598c3c --- /dev/null +++ b/TST/08_Loi_binomiale/exercises.tex @@ -0,0 +1,19 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={Représentation avec des arbres}, step={1}, origin={Création}, topics={Loi binomiale}, tags={Probabilité, Binomiale, Tableur}] + Représenter chacune des situations suivantes par un arbre de probabilité. + \begin{enumerate} + \item Dans mon jardin j'ai planté 3 fraisiers suffisamment éloignés pour qu'ils ne se gênent pas. D'expérience, ils donnent des fruits dans 90\% des cas. Je m'intéresse au nombre de fraisier qui donneront des fruits. + \item Bob mange à la cantine 3 fois par semaine. À chaque fois, il se demande s'il prend un dessert plutôt qu'un fromage ce qu'il fait 2 fois sur 3. On s'intéresse au nombre de fois où il a mangé du dessert en une semaine. + \item Dans un sachet, il reste 6 bonbons: 2 à la fraise et 4 au réglisse. J'en choisi 4 au hasard et je les mange. Je m'intéresse au nombre de bonbon à la fraise que j'ai mangé. + \item Dans un jeu vidéo, j'ai une chance sur 6 de commencer avec un compagnon de type "Terre". Je lance 4 parties et je m'intéresse au nombre de fois où j'ai commencé avec un compagnon de type "Terre". + \item Je joue avec un dé à 6 faces. J'ai le droit à un maximum de 4 lancers. J'arrête de lancer dès que j'ai obtenu un 6. Je compte le nombre de lancer que je fais. + \item Un examen comporte 3 épreuves. On a une chance sur 2 d'avoir la moyenne à l'épreuve de français, 20\% de chance d'avoir la moyenne en histoire et 80\% de chance d'avoir la moyenne en math. On s'intéresse au nombre de fois où l'on peut avoir la moyenne. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Création}, step={1}, origin={Création}, topics={Binomiale et echantillonnage}, tags={Probabilité, Binomiale}] + Proposer une expérience aléatoire qui pourrait être modélisée avec une loi binomiale. Vous détaillerez ensuite les paramètres et justifierez la modélisation. +\end{exercise} + + +\collectexercisesstop{banque} diff --git a/TST/08_Loi_binomiale/index.rst b/TST/08_Loi_binomiale/index.rst new file mode 100644 index 0000000..5317ed9 --- /dev/null +++ b/TST/08_Loi_binomiale/index.rst @@ -0,0 +1,34 @@ +Loi binomiale +############# + +:date: 2021-01-20 +:modified: 2021-01-20 +:authors: Benjamin Bertrand +:tags: Probabilité, Binomiale, Tableur +:category: TST +:summary: Redécouverte de la loi binomiale + +Étape 1: Représentation avec des arbres +======================================= + +Des situations qu'il faut représenter avec des arbres. Toutes les situations ne correspondent pas à la loi binomiale pour ne pas tomber dans la routine. On donne l'exercice aux élèves qui aller chercher dans leurs souvenir pour faire ces arbres. Assez rapidement, on prend un élève qui a réussi pour venir expliquer comment il fait au tableau et débloquer les élèves sans idées. + +Une fois que les arbres sont réalisés (on essayera de tous les faire rentrer sur le tableau). On les compare et extrait ceux qui correspondent à un arbre de loi binomiale pour en fait l'anatomie. + +Les élèves peuvent ensuite créer leur situation modélisable par une loi binomiale. + +.. image:: ./1E_arbres.pdf + :height: 200px + :alt: Situations représentable par un arbre mais pas forcement modélisable par la loi binomiale. + +Bilan: définition de la loi binomiale et représentation par un arbre. + +.. image:: ./1B_definition.pdf + :height: 200px + :alt: définition de la loi binomiale et représentation par un arbre. + +Étape 2: Calculer des probabilités avec des arbres +================================================== + +Étape 3: Simulation avec python +===============================