I have successfully taught a course for gifted high school students (somewhat shorter than yours, about 9 hours) devoted to the probabilistic method (based, naturally, on Alon and Spencer + some other material). I managed to cover the basics, second moment method, some random graphs, games and derandomization. With a little more time I would have squeezed in the Lovasz Local Lemma.

There was a lot of problem solving, but I was also able to show them some more advanced techniques. In general, combinatorics seems to be a good context to introduce some nontrivial probabilistic tools (say, Chernoff-type bounds).

Another probability-based course in the similar format was "random walks and electrical networks". Very nice topic, quite elementary^1, lots of physical intuition - and at the same time, points at the more advanced math beneath (Markov chains, spectral graph theory)

1 - until the kids ask you "wait, how is this probability on the set of infinite trajectories defined? ;) Luckily, I managed to avoid invoking the Kolmogorov extension theorem.