How to analyse chance, ignorance and risk

A hazard of teaching mathematics rather than, say, history is that the homework is a lot harder to come up with. After all, “was Henry VIII a good king?” is a reasonable question to ask either a classroom of nine-year-olds or a lecture theatre of postgraduates. But “solve this quadratic equation” would leave the classroom nonplussed and the lecture theatre unimpressed. Maths is learned by doing, and devising a problem that is easy enough to be accessible, yet hard enough to be satisfying, is a devilish problem itself.