\begin{problem}{Bone Apple CPTeeth} 
Consider the following Bayes net.
\begin{center}
    \includegraphics[height=0.4\textwidth]{figures/bayesnet2.png} 
\end{center}


\begin{question}[6]
If each of the nodes can have 4 possible values, how many entries are in the conditional probability table at that node? 

\vspace{4mm}

\begin{subquestion}[2] A \\
\solutionspace{1cm}{3cm}{Answer:}{\TwoAi}
\end{subquestion}
\begin{subquestion}[2] D \\
\solutionspace{1cm}{3cm}{Answer:}{\TwoAii}
\end{subquestion}
\begin{subquestion}[2] F \\
\solutionspace{1cm}{3cm}{Answer:}{\TwoAiii}
\end{subquestion}
\end{question}

\begin{question}[5]
Which of the following statements are guaranteed to be true? Select all that apply.

\qquad\solution{\emptysquare}{\TwoBA} \quad $B \perp \!\!\! \perp  C$ \quad 

\qquad\solution{\emptysquare}{\TwoBB} \quad $A \perp \!\!\! \perp  F$ \quad 

\qquad\solution{\emptysquare}{\TwoBC} \quad $D \perp \!\!\! \perp  E \mid F$ \quad 

\qquad\solution{\emptysquare}{\TwoBD} \quad $E \perp \!\!\! \perp  A \mid D$ \quad 

\qquad\solution{\emptysquare}{\TwoBE} \quad $F \perp \!\!\! \perp  G \mid D$ \quad 

\qquad\solution{\emptysquare}{\TwoBF} \quad $B \perp \!\!\! \perp  F \mid D$ \quad 

\qquad\solution{\emptysquare}{\TwoBG} \quad $C \perp \!\!\! \perp  G$ \quad 

\qquad\solution{\emptysquare}{\TwoBH} \quad $D \perp \!\!\! \perp  E$ \quad 

\qquad\solution{\emptysquare}{\TwoBI} \quad None of the above.
 \quad 


\end{question}

\end{problem}
