\begin{problem}[10]
Consider the following variation of the Monty Hall game: as usual
there are three doors and a prize hidden behind one door.  But now the
contestant picks \emph{two} doors and Monty's assistant opens one of
the two chosen doors that does not have a prize behind it.

\begin{problemparts}

\problempart[3] Choose the best strategy for the contestant (circle one)

\begin{itemize}
    \item stick with the unopened door
    \item switch to the unchosen door
    \item it doesn't matter
\end{itemize}


\problempart[7] State the probability $p$ of winning with the strategy
you chose above. No proof is necessary.
    
$p =$\brule{1cm}


\solution{
Contestant should stick.  Contestant wins whenever prize is behind one
of his two chosen doors, and probability of this is 2/3.  }

\end{problemparts}
\end{problem}
