\problemdata                                                             
        {Simulating Biased Coins} % latex-friendly label for the prob.
        {Conditional Probability} % The topic(s) of the problem content.  
        {?} % Source (if known)                                          
        {S01 Tutorial 10, 6} % Usage (list ones you are aware of). 
        {Tina Wang, S02} % Last revision info (author, date).   
                                                                         
                                                                         
\begin{problem}           
Suppose you are given a biased coin (probability of heads $p$ with $p$
not necessarily 1/2). Can you devise a procedure to simulate a {\em
fair} coin-flip using the biased coin?

\solution{
Flip the biased coin twice. If the results are the same for the two
flips, continue making two flips of the biased coin until the results
differ. Then say a ``head'' is when the two flips are HT and a
``tail'' is when they're TH. (Unfortunately uses conditional
probability, which we're not up to yet. $p(1-p)=(1-p)p$ and each
divided by their sum (the conditional probability of HT or TH given
it's one of each) is $1/2$.)
}
\end{problem}

                                 