To switch or not to switch

If you’ve not heard of the ‘Monty Hall problem’ read on. In a game show you're given a choice of three doors (say A, B and C). Behind one door is a car and behind the others are goats. Let’s assume you pick door A.

The host, who knows what's behind the doors, opens one of the other doors which has a goat, let’s say door B. You now have the option of switching to the other un-opened door (door C in this case).

The question is will switching doors improve your chances of winning?

Surprisingly, the answer is yes, you should switch. I can see many of you shaking your heads thinking surely there are are two doors left, only one with a car, so the odds of winning are 50-50 no matter which door you pick. Even PhD mathematicians got it wrong when this puzzle was mentioned by Marilyn vos Savant in the US some years ago, she received over 10,000 letters mostly telling her she was wrong.

"May I suggest you obtain and refer to a standard textbook on probability before you try to answer a question of this type again?" (University of Florida)