This might be of interest to people here; it's an example of a genuine confusion over probability that came up in a friends medical research today. It's not particularly complicated, but I guess it's nice to link these things to reality.

My friend is a medical doctor and, as part of a PhD, he is testing peoples sense of smell. He asked if I would take part in a preliminary experiment to help him get to grips with the experimental details.

At the start of the experiment, he places 20 compounds in front of you, 10 of which are type A and 10 of which are type B. You have to select two from that group, smell them, and determine whether they are the same (i.e. both A or both B) or different (one is A, the other B). He's hoping that people will be able to distinguish these two compounds reliably.

It turned out that I was useless at distinguishing them - over a hundred odd trials I managed to hit 50% correct almost exactly. We then discussed the methodology and realised that it was possible to do a little bit better than 50% without any extra sniffing skills.

Any thoughts on how?