The Monty Hall Problem - probabilities and game shows explained

The Monty Hall problem is a famous probability puzzle which Marcus du Sautoy explores with Alan Davies. A game show contestant is invited to choose one of three doors, behind one of which is a good prize (a car) and two of which is a bad prize. The contestant is then shown what's behind one of the two remaining doors and is offered a chance to change their selection. Professor du Sautoy shows through experimental and theoretical probability that the contestant gains a distinct advantage by changing their selection - something that foxed many Mathematicians.