I am supposed to give some 1-hour lectures on interesting topics in probability to an audience that does not know convergence concepts in probability or measure theory (or markov chains, for that matter) but are knowledgeable in real analysis, linear algebra and statistics. Many of them are also knowledgeable in basic number theory.
I am looking for topics to deliver the lectures on. They should not be too technical, neither very gossipy. I do not know much about modern discrete probability; is there something I can teach on modern discrete probability (not the usual combinatorial things found in Feller) which are not really taught as a regular course?