- This course introduces the study of combinatorics. The students will tackle the challenge of identifying and counting the number of different possible ways in which the members of a set (whether they be people, playing cards, numbers, letters, or other discrete entities) can be grouped together subject to various constraints. The concept of “number of possible outcomes” raised by this work leads naturally into an exploration of some basic principles of probability. From this follows a discussion of how we can calculate or estimate probabilities in a wide variety of contexts in our lives. This includes estimating risks and understanding common fallacies in thinking about probability. Finally, we consider conditional probability, and how we can rationally update our estimates of probabilities as we gain new information about the world.
When I was watching Jimmy Kimmel a while back, he had a game with a guest where they had a carton with a dozen eggs. Eight were hard-boiled. Four were still raw. You took turns drawing an egg out of the carton and smashing it full speed on the top of your head. Whoever was the first to smash two raw eggs on themselves lost. He calls it Egg Russian Roulette.
Always seemed to me like it would be an incredibly fun introduction to Probability. You can SEE that your chances of getting egg on your head increase with every hard-cooked egg that smashes and causes no damage. You literally calculate mentally as you're picking up the egg (and picking it up and putting it back after you feel it is not allowed) what your chances are of being covered in slick egg innards. The audience is doing those mental calculations too.
Of course, you could do this by dropping the eggs out of the window onto your concrete patio, too, or throwing them at the barn door. There's no rule that says you have to smash them on yourself. But I think it would be fun and a lesson no 9th grader (or middle schooler) would ever forget.