Question

I think that presenting the connection between random walks and electrical networks (like in the classic text "Random walks and electric networks" by Doyle and Snell) is an interesting and feasible idea. Just a week ago I taught a 6-day course about this to talented high schoolers and it worked out very nicely. It's a good opportunity to show them interesting applications of probability and give a flavour of a vibrant field of mathematics. Plus, there is a quite a lot of room for digressions on Markov chains, spectral graph theory etc.