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a/1ST/04_Repetition_dexperiences/2B_proba_arbre.tex b/1ST/04_Repetition_dexperiences/2B_proba_arbre.tex index 1061b8c..859eada 100644 --- a/1ST/04_Repetition_dexperiences/2B_proba_arbre.tex +++ b/1ST/04_Repetition_dexperiences/2B_proba_arbre.tex @@ -9,7 +9,6 @@ \begin{document} -\maketitle \setcounter{section}{1} \section{Calculer des probabilités dans les arbres} @@ -56,5 +55,52 @@ On lance deux fois une pièce déséquilibré qui a 2 chance sur 3 de faire pile \end{tikzpicture} \end{center} -\afaire{Compléter les noeuds puis les probabilités sur l'arbre.} +\vfill + +\setcounter{section}{1} +\section{Calculer des probabilités dans les arbres} + +\begin{propriete}[Probabilités dans les arbres] + \begin{itemize} + \item La somme des probabilités des branches issues d'un même noeud est égale à 1. + \item La probabilité d'un chemin est égale au produit des probabilités des branches parcourues. + \item La probabilité d'un évènement est égale à la somme des probabilités des chemins qui conduisent à cet évènement. + \end{itemize} +\end{propriete} + +\paragraph{Exemples:}~ +On lance deux fois une pièce déséquilibré qui a 2 chance sur 3 de faire pile. + +\begin{center} + \begin{tikzpicture}[grow=down, sloped, scale=1.5] + \node {.} + child [red] {node {.} + child {node {.} + edge from parent + node[above] {.} + } + child [black] {node {.} + edge from parent + node[above] {.} + } + edge from parent + node[above] {.} + } + child[missing] {} + child { node {.} + child {node {.} + edge from parent + node[above] {.} + } + child {node {.} + edge from parent + node[above] {.} + } + edge from parent + node[above] {.} + }% + ; + \end{tikzpicture} +\end{center} +\vfill \end{document}