The Monty Hall problem

I seem to have started something with all this talk of probability, risk and such (see my previous Aardvark post), and a number of people have asked me for another counter-intuitive probability puzzle. Well perhaps the most baffling is the Monty Hall problem. This is based on a game show where a contestant is faced with three doors. Behind two of the doors are goats; behind the third is a car – the star prize. The contestant is asked to pick a door, but before it’s opened, the host, who knows what is behind each of the doors, opens one of the other doors to reveal a goat. The contestant is then asked if they want to change their mind about the door they want to open. What’s the best thing to do? Most people reason that since it’s now down to two doors, which looks like a 50% chance of winning the car (after-all, it must be behind one of the doors), there’s no point in changing. Wrong! Changing actually increases your chance of winning to 66.6%. Why? Have a good think about it and when you want to know the answer just search for the Monty Hall problem on Google… the whole thing has become strangely controversial!