What is the probability that at least two people in a group of 20 people will have the same birthday? - David Franklin

I guess… it was just a shocking event. We’re not used to someone like him being President.” Here, the student reveals an availability bias in which we expect future outcomes to look like what has gone before.

He asks the 80 students to respond based on their ‘gut feeling’. Again, students are given five options, ranging from ‘less than 1%’ to ‘above 40%’. About half of them believe the true answer is less than 5%, of which plenty go for the ‘less than 1%’ option. Only 1 in 6 get it right, picking the highest option: it turns out that the true figure is 41%. He invites those people – 13 in total – to stand up.

So Trump was 29% likely to win. What does 29% mean?” he asks. This is an odd question for many: they’re doing a Master’s degree at Harvard, and they’re being asked what a percentage means. The question is aiming at the gut reaction of the brain to the number. Inevitably, students think it might be a trick question. Dan waits a while, and when no-one raises their hands, he breaks away from the example to tell a story: “You know, when I first started teaching, I was terrified of silence. I thought, ‘oh my god, I’ve got to do something, they’re not saying anything’.” The class laughs: he has eased the tension created by the silence. “The more I taught, the more I realised that silences are important in a class – they give time for people to think. These days, I’m not afraid of silence at all.” After a few seconds, a woman puts up her hand. “Well, obviously, I knew that it meant there was some chance that he would win. But it was still a shock that the 29% happened.