\problemdata                                                             
        {Dungeons and Dragons} % latex-friendly label for the prob.
        {Probability with Counting} % The topic(s) of the problem content.  
        {?} % Source (if known)                                          
        {S01 Tutorial 10, 1} % Usage (list ones you are aware of). 
        {Tina Wang, S02} % Last revision info (author, date).   
                                                                         
                                                                         
\begin{problem}           
A Dungeons and Dragons player rolls several dice and sums the results
to determine how many points of damage his warrior does to a
fire-breathing dragon.  If the warrior does $20$ or more points of
damage, then the dragon is slain.  If the warrior does fewer than $20$
points of damage, then the dragon survives and makes a nice pot-roast
out of the warrior.  What is the probability that the warrior survives
if:

\begin{problemparts}
\problempart The player rolls two 12-sided dice.
\solution{${15}/{12^2} = 0.104$. (We're counting the number of dice
rolls with sum $\ge20$. The first die must be $\ge 8$. If it's $8$,
there's $1$ possibility for the second die; if $9$, $2$ possibilities,
up to if $12$, $5$ possibilities for a total of $15$.)}

\problempart The player rolls three 8-sided dice.
\solution{$35/8^3 = 0.068$. (We're counting the number of dice rolls
with sum $\ge20$. The first die must be $\ge 4$. If it's $4$, there's
$1$ way to choose the other dice; if it's $5$, $1+2$ ways, up to if
$8$, $1+2+3+4+5$ ways, for a total of $35$.)}

\end{problemparts}
\end{problem}

                                 