I remember a few months ago there was a discussion on one of the mailing lists about the Monty Hall problem (there is an exhaustive explanation on Wikipedia - including the Bayesian solution). I first came across this problem at University when the question was posed in a 100 level psychology paper. The next time I heard of it was when it was discussed in the 2003 Whitbread Book of the Year novel "The Curious Incident of the Dog in the Night-Time". This book is told in the first person by a 15 year old boy with Asperger's Syndrome, and covers mathematical aspects from Chaos Theory to prime numbers - and highlights the fact that most people are surprised at the ultimately correct answer to the Monty Hall problem.

Apparently I'm a nerd - but ever since that first exposure to the Monty Hall problem it's become a bit of a social game for me to pose the problem to friends and watch the pleased look on their faces as they work it out. So, for all those who have not heard of the problem before, give this probability puzzle a go:

Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Is it to your advantage to change your choice? (Krauss and Wang 2003:10)

Esther Meenken

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