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d'issues d'une expérience aléatoire est appelée \textbf{évènement}. + + On les décrit en général avec une letter capitale. On liste ou l'on décrit les issues en accolades $\{... \}$ +\end{definition} + +\paragraph{Exemples}: +\begin{itemize} + \item On se place dans le cadre de l'expérience aléatoire des accidents des piétons. Des évènements peuvent être + \begin{itemize} + \item $A = \left\{ \mbox{accidents peu graves avec un casque}\right\}$ + \item $B = \left\{ \mbox{accidents sans casque ou graves}\right\}$ + \end{itemize} + \item On lance un dé à 10 faces. Des évènements peuvent être + \begin{itemize} + \item + \item + \end{itemize} +\end{itemize} +\afaire{proposer des évènements} + +\begin{propriete} + La probabilité d'un évènement est égale à la somme des probabilités des issues qui le constituent. +\end{propriete} + +\begin{propriete}[Cas d'une loi équiprobable] + Si l'on considère une expérience aléatoire modélisable par une loi équiprobable alors la probabilité d'une évènement $A$ se calcule + \[ + P(A) = \frac{\mbox{Nombre d'issues dans }A}{\mbox{Nombre total d'issue}} + \] +\end{propriete} + +\begin{definition} + \begin{itemize} + \item Un évènement est dit \mbox{élémentaire} quand il est constitué d'une unique issue. + \item Un évènement est dit \mbox{certain} quand il contient toutes les issues. Sa probabilité est ainsi égale à 1. + \item Un évènement est dit \mbox{impossible} quand il est constitué d'issues dont les probabilités sont égales à 0. + \end{itemize} +\end{definition} + +\end{document} diff --git a/2nd/05_Introduction_Probabilites/index.rst b/2nd/05_Introduction_Probabilites/index.rst index fcb1a70..2b3a4de 100644 --- a/2nd/05_Introduction_Probabilites/index.rst +++ b/2nd/05_Introduction_Probabilites/index.rst @@ -38,6 +38,11 @@ Situation et tableau de fréquences. Bilan: Vocabulaire autour des évènements +.. image:: ./2B_evenements.pdf + :height: 200px + :alt: Cours sur les évènements + + Étape 3: Lancé de deux dés ==========================