From 383f698289f130291013571482f0c127df9138c8 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 1 Nov 2021 11:21:25 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20Bilan=20sur=20la=20loi=20de=20probabili?= =?UTF-8?q?t=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/05_Introduction_Probabilites/1B.tex | 14 --- .../1B_loi_probabilites.pdf | Bin 0 -> 44371 bytes .../1B_loi_probabilites.tex | 84 ++++++++++++++++++ 2nd/05_Introduction_Probabilites/index.rst | 15 +++- 4 files changed, 97 insertions(+), 16 deletions(-) delete mode 100644 2nd/05_Introduction_Probabilites/1B.tex create mode 100644 2nd/05_Introduction_Probabilites/1B_loi_probabilites.pdf create mode 100644 2nd/05_Introduction_Probabilites/1B_loi_probabilites.tex diff --git a/2nd/05_Introduction_Probabilites/1B.tex b/2nd/05_Introduction_Probabilites/1B.tex deleted file mode 100644 index 3e6848c..0000000 --- a/2nd/05_Introduction_Probabilites/1B.tex +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[a4paper,10pt]{article} -\usepackage{myXsim} - -\author{Benjamin Bertrand} -\title{Introduction Probabilites - Cours} -\date{2021-08-25} - -\pagestyle{empty} - -\begin{document} - -\maketitle - -\end{document} diff --git a/2nd/05_Introduction_Probabilites/1B_loi_probabilites.pdf b/2nd/05_Introduction_Probabilites/1B_loi_probabilites.pdf new file mode 100644 index 0000000000000000000000000000000000000000..da0d91e37b9f470dbe8373b0abb70ea6ccdf0e85 GIT binary patch literal 44371 zcmce-W2`XUwl27A+qP}nwr$%s-(}n8yKLLGZF}{%&$%akJKag&KYP!lDzoMoHB(QX zQKK?YqzWQpw2XADP^5E9!)s711PlcBMpjTfJW%v1o(`r2^cwO;R;I=-Q1r^KMlS!g zB4+Po3q>y^WbZ+s&G3&tBg20kx={50lKj_Qj8OElhAvK)|7bA&qw$aYU*~@`luVuN zU7d_goe5a~Sy6(bmoc?7cd;N~WF`1tzaE|apN;=B5IFu_5IFy15E%bO&cB5Q z#(z=%pW%U#>E8z8KW9vg|2Au4`WMIl877$iMf$(RoS2yZb0GfZ1phrC*#2`M{$;uU z77)z;`#bT!+&44RKg|Ev`2Tm`*EqWIn`{rh{-JYeYXVab+9tcTvUC=TdyTSiuX9g= z4JktbH1;;stDmpzgY=4xSJj6$fnZr=DJ;cdgZmDAl#2(xg3;*gE>?7n$ty^f9`|0VUwohKyjLgH*|zH2 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toutes les \textbf{issues} sont connues sans que l'on puisse déterminer laquelle sera \textbf{réalisée}. + + L'ensemble des issues est appelée \textbf{univers}. On le note en général $\Omega$ (oméga) ou $E$. +\end{definition} + +\paragraph{Exemples} +\begin{itemize} + \item Programme de l'ordinateur + \item Accident à pied + \item Lancer un dé à 6 faces et observer le résultat +\end{itemize} +\afaire{Pour les 3 expériences, décrire l'univers et donner l'exemple de quelques issues.} + +\begin{definition}{Loi de probabilité} + Une expérience aléatoire peut être modélisée avec une \textbf{loi de probabilité}. + + Pour cela, on va associer à toutes les issues de cette expérience un nombre compris entre 0 et 1 de sorte à ce que la somme de ces nombres face 1. + + Ce nombre modélisera la \textbf{probabilité} de l'issue. Plus ce nombre est proche de 0 moins l'issue aura de chance d'être réalisé. Plus il sera proche de 1 plus l'issue aura de chance d'être réalisé. +\end{definition} + +\paragraph{Remarques} +\begin{itemize} + \item On peut représenter cette loi avec un tableau avec une ligne où l'on liste toutes les issues et une autre où l'on associe les probabilités. + \item Dans la pratique, déterminer une loi de probabilité est quelque chose de très dur. +\end{itemize} + +\paragraph{Exemples de loi de probabilité} + +\begin{multicols}{2} + \begin{itemize} + \item Programme de l'ordinateur + + \begin{tabular}{|p{2cm}|p{1cm}|p{1cm}|} + \hline + Issues & & \\ + \hline + Probabilités & & \\ + \hline + \end{tabular} + \item Dé à 6 faces + + \begin{tabular}{|p{2cm}|*{6}{p{0.5cm}|}} + \hline + Issues & & & & & &\\ + \hline + Probabilités & & & & & & \\ + \hline + \end{tabular} + \end{itemize} +\end{multicols} +\afaire{Pour les 3 expériences, décrire l'univers et donner l'exemple de quelques issues.} + + +\begin{definition}[ Loi équirépartie ] + Quand toutes les issues ont la même probabilité, on dit alors que la loi est \textbf{équirépartie}. Dans ce cas, cette probabilité vaut + \[ + \frac{1}{\mbox{nombre total d'issue}} + \] +\end{definition} + +\paragraph{Exemples:} +\afaire{Donner des exemples d'expériences aléatoire modélisables avec une loi équirépartie} + +\paragraph{Remarque:} il existe d'autre loi de probabilités "remarquable" comme celle là. Elles ne seront pas étudiées avant la terminale. + + +\end{document} diff --git a/2nd/05_Introduction_Probabilites/index.rst b/2nd/05_Introduction_Probabilites/index.rst index ec67bf6..4726ca1 100644 --- a/2nd/05_Introduction_Probabilites/index.rst +++ b/2nd/05_Introduction_Probabilites/index.rst @@ -2,7 +2,7 @@ Introduction Probabilités ######################### :date: 2021-08-25 -:modified: 2021-10-18 +:modified: 2021-11-01 :authors: Benjamin Bertrand :tags: Probabilité :category: 2nd @@ -13,15 +13,26 @@ Introduction Probabilités Exercices type `exercice de Djelan `_ avec des situations un peu plus complexes. +.. image:: ./1E_situations_critiques.pdf + :height: 200px + :alt: 3 situations avec de grands périles + Les élèves vont être amené à redéfinir la notion de probabilité et pourront réinvestir leur connaissances sur les factions pour comparer ces quantités. -Bilan: vocabulaire et de la formule des probabilité +Bilan: Vocabulaire sur la loi de probabilités + +.. image:: ./1B_loi_probabilites.pdf + :height: 200px + :alt: Bilan sur les lois de probabilités + Étape 2: Exercices classiques ============================= Situation et tableau de fréquences. +Bilan: Vocabulaire autour des évènements + Étape 3: Lancé de deux dés ==========================