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\title{General Mathematics and Computational Science I}
\author{Exercise 13}
\date{October 25, 2005}
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\begin{enumerate}

\item Suppose you meet $n$ random people (excluding yourself).

\begin{enumerate}
\item What is the probability that at least one of them is born on the
same day of the year as you?
\item How large should $n$ be so that this happens with a probability
of at least $\tfrac12$?
\end{enumerate}

\item Prove the \emph{arithmetic-geometric-mean inequality} for $n=3$.

Note: This is Problem 9 from Ivanov, p.\ 48, which contains a sketch
of a proof.  The task here is to write out a complete self-contained
solution without reference to Ivanov.

\end{enumerate}
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