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+ % This file is public domain
+ %
+ % These problems are a mixture of essay-style and questions with
+ % answers. One of these problems requires the tikz package
+
+\newproblem*{oop}{Describe what is meant by object-oriented
+programming.}
+
+\begin{defproblem}{inheritance}
+ Describe what is meant by the term \emph{inheritance} in
+ object-oriented programming. Use examples.
+\end{defproblem}
+
+\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}
+
+\begin{defproblem}{digraph}
+ \begin{onlyproblem}\label{ex:digraph}
+ Identify, if any, the sinks and sources of the digraph shown in Figure~\ref{fig:digraph}.
+
+ \begin{figure}[tbh]
+ \centering
+ \begin{tikzpicture}[every node/.style={draw,circle}]
+ \path (0,0) node (A) {$A$}
+ (1,0) node (B) {$B$}
+ (0,1) node (C) {$C$};
+ \draw[->] (A) -- (B);
+ \draw[->] (B) -- (C);
+ \draw[->] (A) -- (C);
+ \end{tikzpicture}
+ \par
+ \caption{Digraph for Question~\ref{ex:digraph}}
+ \label{fig:digraph}
+ \end{figure}
+ \end{onlyproblem}
+ \begin{onlysolution}
+ $A$ is a souce and $C$ is a sink.
+ \end{onlysolution}
+\end{defproblem}