(for 3 Quarks Daily)
It’s my favorite topic of the year, I tell the kids, before scanning my conscience for signs that I have just lied to them. No, this feels about right, and in any case, they didn’t need my reassurance: after a dry unit about ratios, at my mention of the word “probability” I can practically hear the sound of neurons firing. Whether they know of any contexts in which chance turns up? Boy, do they. My twelve-year old students inform me about dice, cards, spinners, lotteries, casinos, about your chances of survival in Squid Game, about unearthing rare minerals in Minecraft, and about whether the stuff you want to buy is actually in stock because sometimes they run out and there’s no telling in advance when. Also the weather.
I love introducing them to the math of probability precisely because it is a topic that they have already thought about so much, but that I know many of them have incoherent intuitions about. Not that I don’t, of course, but I am a little bit ahead of them and I know from experience what I am working with. Somebody will opine that the chance that it’s going to rain next month is “fifty-fifty” because it either will or it won’t. Somebody will say that there is a 1/7 chance that someone’s favorite day of the week is Thursday. Somebody will reason that since the highest sum you can roll with two D6-dice is a 12, the chance you roll a 10 is 1 in 12, which…
Oh wait, is it? Anyway, you get the point: the process feels properly Socratic, taking slightly muddled concepts that students already feel strongly about, and providing the right nudges to make them reconsider some of those concepts and make others click together. It is a significant source of satisfaction every year to see just how fast ‘the group’ moves from guessing that a sequence of three coin flips has six possible outcomes (unless it can land on its side, which they also unerringly point out), to calculating the number of four-digit pin codes where all the digits have to be different.
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