Monty Hall

This is a continuation of the previous post under this title.

Most people reason that, as there are now only two doors the car can be behind, it's a 50-50 chance, and therefore swopping doors makes no difference. In fact, the answer is, you should swop doors, because by so doing, you double your chances of winning the car. Perhaps the easiest way of explaining it is like this - you started out with three doors, and assuming the car is put behind one of these doors at random, you have a one-in-three chance of picking the right door. I think (hope) we can all agree on that. But this means that there is a two-in-three chance that you are wrong - that the car is somewhere else. At this point, that "somewhere else" is either Door B or door C. But once Monty Hall opens Door B and shows the car is not there, that "somewhere else" has to be Door C. You still have - always had and always will have - a one-third chance of choosing the right door in the first place, but if you were wrong (two-thirds chance) you now know where the car is! So swop doors.

But next time we'll look at what happens if we introduce a new contestant into the mix........