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\def\doctitle{}
\def\topictitle{\textsc{Juego de dados}}
\def\theauthor{E. Barrios}
\def\course{\textsc{}}
\def\period{Febrero 2015}
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\input{juegoDados2-concordance}

\begin{enumerate}

\item []{\bf Ejercicio 2.119} \quad Suponga que se lanzan repetidamente dos
dados y se cuenta la suma de las caras hacia arriba en cada lanzamiento.
Determine la probabilidad de los siguientes eventos:
\begin{enumerate}[\it a)]
\item La suma 3 sale antes que la suma 7.
\item La suma 4 sale antes que la suma 7.
\end{enumerate}

\Solucion:

\begin{enumerate}[\it a)]
\item
Considere los eventos:
\[\begin{array}{rcl}
S_j & = & \{\text{Suma es j}\} \\
T_k & = & \{\text{El juego termina en el ensayo $k$}\} \\
G_3 & = & \{\text{Sale el 3 antes que el 7}\} \\
\end{array} \]
Entonces,
\[
G_3 = \bigcup_{k=1}^{\infty}(S_3 \cap T_k)
\]
con los eventos $(S_3\cap T_k)$ ajenos. Luego,
\[
\Pr(G_3) = \sum_{k=1}^{\infty}\Pr(S_3\cap T_k)
\]


\end{enumerate}


\end{enumerate}


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