\begin{exercice}[Le pari du Chevalier de Méré][\tice]
Le problème dit du \og pari du chevalier de Méré\fg{} opposa ce dernier à Fermat et à Pascal :
%\vspace{-0.5em}
\begin{itemize}
\item \textit{Pari 1 :} si l'on jette 4 fois un dé à 6 faces, il y a plus de chances qu'on obtienne un six plutôt qu'on n'en obtienne pas.
\item \textit{Pari 2 :} si l'on jette 24 fois deux dés à 6 faces, il y a aussi plus de chances qu'on obtienne un double six qu'on n'en obtienne pas.
\end{itemize}
\vspace{-1em}
\begin{center}
Que penser de ces deux paris?
\end{center}
\vspace{-2em}
\begin{enumerate}
\item \`A l'aide d'un tableur, on simule 500 lancers de 4 dés à 6 faces.
Voici une capture d'écran. 
\begin{tableau}[lc]{\linewidth}{7}
     \hline	 &A&B&C&D&E&F\\
\hline
1&dé 1&dé 2&dé 3&dé 4&&\\
\hline
2&3&5&6&3&&\u{0.498}\\
\hline 
3&5&1&1&4&0&\\
\hline
\end{tableau}
\vspace{-1.5em}
\begin{enumerate}
\item Proposer une formule pour simuler le lancer d'un dé, à saisir en \texttt{A2},  \texttt{B2}, \texttt{C2} et \texttt{D2}.
\item Que calcule l'instruction \texttt{NB.SI(A2:D2;6)}? \\
Qu'affiche la cellule \texttt{E2} si on entre \\\texttt{=SI(NB.SI(A2:D2;6) >1;1;0)}?
\item Que calcule la formule  \texttt{=NB.SI(E2:E501;1)/500},  à saisir en cellule \texttt{F2}?
\item Compléter la feuille de calcul. \\ Donner la fréquence d'apparition d'un six et l'intervalle de confiance associé.\\ Que pouvez-vous conclure du \textit{Pari 1}?
\end{enumerate}
\vspace{-1.5em}
\item Simuler \nombre{1000} puis \nombre{10000} expériences. \\Que peut-on conclure du \textit{Pari 1}?
\item On simule \nombre{1000} lancers de 24~fois deux dés à 6 faces. Le graphique ci-dessous donne l'évolution des\\ fréquences d'apparition  en \upc{} d'un double six.\\
Que penser du \textit{Pari 2}?
\end{enumerate}
\vspace{-1.5em}
\begin{center}
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\axeX[47]{0}{105}{0,20,40,60,80,100}
\axeY{47}{56}{47,49,51,53, 55}
\draw (105,45.5) node[left] {(en centaines de lancers)};


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 \draw(82.25,49.604863221885)node{$\bullet$};   
 
 \draw(82.5,49.636363636364)node{$\bullet$};   
 
 \draw(82.75,49.655589123867)node{$\bullet$};   
 
 \draw(83,49.650602409639)node{$\bullet$};   
 
 \draw(83.25,49.633633633634)node{$\bullet$};   
 
 \draw(83.5,49.616766467066)node{$\bullet$};   
 
 \draw(83.75,49.683582089552)node{$\bullet$};   
 
 \draw(84,49.72619047619)node{$\bullet$};   
 
 \draw(84.25,49.709198813056)node{$\bullet$};   
 
 \draw(84.5,49.680473372781)node{$\bullet$};   
 
 \draw(84.75,49.675516224189)node{$\bullet$};   
 
 \draw(85,49.670588235294)node{$\bullet$};   
 
 \draw(85.25,49.66568914956)node{$\bullet$};   
 
 \draw(85.5,49.672514619883)node{$\bullet$};   
 
 \draw(85.75,49.644314868805)node{$\bullet$};   
 
 \draw(86,49.651162790698)node{$\bullet$};   
 
 \draw(86.25,49.669565217391)node{$\bullet$};   
 
 \draw(86.5,49.722543352601)node{$\bullet$};   
 
 \draw(86.75,49.729106628242)node{$\bullet$};   
 
 \draw(87,49.712643678161)node{$\bullet$};   
 
 \draw(87.25,49.74212034384)node{$\bullet$};   
 
 \draw(87.5,49.737142857143)node{$\bullet$};   
 
 \draw(87.75,49.74358974359)node{$\bullet$};   
 
 \draw(88,49.704545454545)node{$\bullet$};   
 
 \draw(88.25,49.688385269122)node{$\bullet$};   
 
 \draw(88.5,49.672316384181)node{$\bullet$};   
 
 \draw(88.75,49.645070422535)node{$\bullet$};   
 
 \draw(89,49.629213483146)node{$\bullet$};   
 
 \draw(89.25,49.647058823529)node{$\bullet$};   
 
 \draw(89.5,49.664804469274)node{$\bullet$};   
 
 \draw(89.75,49.649025069638)node{$\bullet$};   
 
 \draw(90,49.622222222222)node{$\bullet$};   
 
 \draw(90.25,49.584487534626)node{$\bullet$};   
 
 \draw(90.5,49.635359116022)node{$\bullet$};   
 
 \draw(90.75,49.69696969697)node{$\bullet$};   
 
 \draw(91,49.67032967033)node{$\bullet$};   
 
 \draw(91.25,49.687671232877)node{$\bullet$};   
 
 \draw(91.5,49.661202185792)node{$\bullet$};   
 
 \draw(91.75,49.66757493188)node{$\bullet$};   
 
 \draw(92,49.695652173913)node{$\bullet$};   
 
 \draw(92.25,49.70189701897)node{$\bullet$};   
 
 \draw(92.5,49.708108108108)node{$\bullet$};   
 
 \draw(92.75,49.703504043127)node{$\bullet$};   
 
 \draw(93,49.677419354839)node{$\bullet$};   
 
 \draw(93.25,49.630026809651)node{$\bullet$};   
 
 \draw(93.5,49.625668449198)node{$\bullet$};   
 
 \draw(93.75,49.642666666667)node{$\bullet$};   
 
 \draw(94,49.617021276596)node{$\bullet$};   
 
 \draw(94.25,49.580901856764)node{$\bullet$};   
 
 \draw(94.5,49.566137566138)node{$\bullet$};   
 
 \draw(94.75,49.540897097625)node{$\bullet$};   
 
 \draw(95,49.536842105263)node{$\bullet$};   
 
 \draw(95.25,49.501312335958)node{$\bullet$};   
 
 \draw(95.5,49.465968586387)node{$\bullet$};   
 
 \draw(95.75,49.483028720627)node{$\bullet$};   
 
 \draw(96,49.458333333333)node{$\bullet$};   
 
 \draw(96.25,49.454545454545)node{$\bullet$};   
 
 \draw(96.5,49.481865284974)node{$\bullet$};   
 
 \draw(96.75,49.467700258398)node{$\bullet$};   
 
 \draw(97,49.453608247423)node{$\bullet$};   
 
 \draw(97.25,49.470437017995)node{$\bullet$};   
 
 \draw(97.5,49.435897435897)node{$\bullet$};   
 
 \draw(97.75,49.432225063939)node{$\bullet$};   
 
 \draw(98,49.408163265306)node{$\bullet$};   
 
 \draw(98.25,49.35368956743)node{$\bullet$};   
 
 \draw(98.5,49.329949238579)node{$\bullet$};   
 
 \draw(98.75,49.296202531646)node{$\bullet$};   
 
 \draw(99,49.292929292929)node{$\bullet$};   
 
 \draw(99.25,49.329974811083)node{$\bullet$};   
 
 \draw(99.5,49.356783919598)node{$\bullet$};   
 
 \draw(99.75,49.37343358396)node{$\bullet$};   
 
 \draw(100,49.33)node{$\bullet$};   
\end{footnotesize}
 
\end{tikzpicture}
\end{center}
\vspace{-1.5em}
\end{exercice}