Professor Rosencrantz flips a fair coin. Professor Guildenstern flips a fair coin twice. What is the probability that Professor Rosencrantz obtains more heads than professor Guildenstern?

Let us call $G_n$ and $R_n$ the number of heads each professor has. The answer is:

$$ \Pr\{R_n = 1\}.\Pr\{G_n = 0\} = \frac{1}{2}.\frac{1}{4} = \frac{1}{8} $$