Monty Hall.

This is a continuation of the previous posts under this title.
So you've chosen Door A, Monty Hall has opened Door B and shown it to be empty, and you have now announced your intention to swop to Door C, having calculated that this gives you a two-out-of-three chance of winning the car. At this point, let's suppose a new contestant is introduced - call him or her Contestant II. They have never seen this game before, and have been in a sound-proof booth up until now, so have no idea of what's going on. They are simply presented with a closed door, an open door and a closed door, and told that behind one of the closed doors is a car, which they will win if they pick the correct door. They choose Door C. What is their chance of success? Well, they will have no reason to think that the car is behind one door any more than the other, so they'll go eeny-meeny-miny-moe, and pick Door C with a 50-50 chance. So here's the paradox - you have both picked Door C, but you have a two-thirds chance of being right, whereas they only have a one-half chance of being right. How can this be? To explain this, we have to look rather more deeply into just what probability means, and how it works, and we'll do that next time.