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diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/probspaces2.tex b/Master/texmf-dist/doc/latex/probsoln/samples/probspaces2.tex deleted file mode 100644 index 26839b65293..00000000000 --- a/Master/texmf-dist/doc/latex/probsoln/samples/probspaces2.tex +++ /dev/null @@ -1,41 +0,0 @@ - % Finite probability spaces -\begin{defproblem}{weightedcoin} -\begin{onlyproblem}% -A coin is weighted so that heads is four times as likely -as tails. Find the probability that: -\begin{textenum} -\item tails appears, -\item heads appears -\end{textenum} -\end{onlyproblem} -\begin{onlysolution}% -Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$, -so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore: -\begin{textenum} -\item $P(T)=\frac{1}{5}$, -\item $P(H)=\frac{4}{5}$ -\end{textenum} -\end{onlysolution} -\end{defproblem} - -\begin{defproblem}{validprobspaces} -\begin{onlyproblem}% -Under which of the following functions does -$S=\{a_1,a_2\}$ become a probability space? -\par -\begin{textenum} -\begin{tabular}{ll} -\item $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ -& -\item\label{validprobspacescorrect1} $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$ -\\ -\item\label{validprobspacescorrect2} $P(a_1)=1$, $P(a_2)=0$ -& -\item $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ -\end{tabular} -\end{textenum} -\end{onlyproblem}% -\begin{onlysolution}% -\ref{validprobspacescorrect1} and \ref{validprobspacescorrect2}% -\end{onlysolution} -\end{defproblem} |