
\begin{enumerate}
\item On a l'arbre suivant :

\begin{minipage}{0.7\linewidth}
\begin{center}
\begin{tikzpicture}[rotate=-90]
\node (U) at (0,2.5) {1};
\node (D) at (0,0) {2};
\node (T) at (0,-2.5) {3};
%
\node (UU) at ($(U)+(2,0.85)$) {1};
\node (UD) at ($(U)+(2,0)$) {2};
\node (UT) at ($(U)+(2,-0.85)$) {3};
\node (DU) at ($(D)+(2,0.85)$) {1};
\node (DD) at ($(D)+(2,0)$) {2};
\node (DT) at ($(D)+(2,-0.85)$) {3};
\node (TU) at ($(T)+(2,0.85)$) {1};
\node (TD) at ($(T)+(2,0)$) {2};
\node (TT) at ($(T)+(2,-0.85)$) {3};
%
\node (UUA) at ($(UU)+(2,0.25)$) {A};
\node (UUB) at ($(UU)+(2,-0.25)$) {B};
\node (UDA) at ($(UD)+(2,0.25)$) {A};
\node (UDB) at ($(UD)+(2,-0.25)$) {B};
\node (UTA) at ($(UT)+(2,0.25)$) {A};
\node (UTB) at ($(UT)+(2,-0.25)$) {B};
\node (DUA) at ($(DU)+(2,0.25)$) {A};
\node (DUB) at ($(DU)+(2,-0.25)$) {B};
\node (DDA) at ($(DD)+(2,0.25)$) {A};
\node (DDB) at ($(DD)+(2,-0.25)$) {B};
\node (DTA) at ($(DT)+(2,0.25)$) {A};
\node (DTB) at ($(DT)+(2,-0.25)$) {B};
\node (TUA) at ($(TU)+(2,0.25)$) {A};
\node (TUB) at ($(TU)+(2,-0.25)$) {B};
\node (TDA) at ($(TD)+(2,0.25)$) {A};
\node (TDB) at ($(TD)+(2,-0.25)$) {B};
\node (TTA) at ($(TT)+(2,0.25)$) {A};
\node (TTB) at ($(TT)+(2,-0.25)$) {B};
%
\draw (-2,0) -- (U.north);
\draw (-2,0) -- (D.north);
\draw (-2,0) -- (T.north);
\draw (U.south) -- (UU.north);
\draw (U.south) -- (UD.north);
\draw (U.south) -- (UT.north);
\draw (D.south) -- (DU.north);
\draw (D.south) -- (DD.north);
\draw (D.south) -- (DT.north);
\draw (T.south) -- (TU.north);
\draw (T.south) -- (TD.north);
\draw (T.south) -- (TT.north);
\draw (UU.south) -- (UUA.north);
\draw (UU.south) -- (UUB.north);
\draw (UD.south) -- (UDA.north);
\draw (UD.south) -- (UDB.north);
\draw (UT.south) -- (UTA.north);
\draw (UT.south) -- (UTB.north);
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\draw (DT.south) -- (DTB.north);
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\draw (TD.south) -- (TDA.north);
\draw (TD.south) -- (TDB.north);
\draw (TT.south) -- (TTA.north);
\draw (TT.south) -- (TTB.north);
\end{tikzpicture}
\end{center}
\end{minipage}
\begin{minipage}{0.25\linewidth}
\uline{Il y a donc 18 codes possibles.}
\end{minipage}



\item 
\begin{itemize}
\item $\proba{A}=\dfrac{1}{18}$ : il n'y a qu'un code \og 33A \fg{}  sur les 18 codes possibles.
\item $\proba{B}=\dfrac{6}{18}=\dfrac{1}{3}$ car il y a 6 codes commençant par 2.
\item $\proba{C}=\dfrac{1}{2}$ : il y a 1 code sur 2 qui finit par A.
\item $\proba{D}=\dfrac{6}{18}=\dfrac{1}{3}$ : seuls les codes 11A, 11B, 22A, 22B, 33A et 33B conviennent.
\item $\proba{E}=\dfrac{4}{18}=\dfrac{2}{9}$ : seuls les codes 22A, 23A, 32A et 33A ne contiennent ni le 1, ni le B.
\end{itemize}
\end{enumerate}
