Most people get this wrongeven
Most people get this wrongeven those with formal mathematics training. Many of the thousands who wrote to Marilyn vos Savant at Parade were university professors who were convinced that she had got it wrong and insisted she was misleading the nation. Even the famous Paul Erdos, years before the Parade magazine incident, had got the answer wrong and he was one of the most talented mathematicians of the century (and inspiration for Erdos numbers, which you may have heard of3).
The answer is that you should switchyou are twice as likely to win the prize if you switch doors than if you stick with your original door. Don’t worry if you can’t see why this is the right answer; the problem is famous precisely because it is so hard to get your head around. If you did get this right, try telling it to someone else and then explaining why switching is the right answer. You’ll soon see just how difficult the concepts are to get across.
7.3.2. How It Works
The chance you got it right on the first guess is 1 in 3. Since by the time it comes to sticking or switching, the big prize (often a car) must be behind one of the two remaining doors, there must be a 2 in 3 chance that the car is behind the other door (i.e., a 2 in 3 chance your first guess was wrong).
Our intuition seems compelled to ignore the prior probabilities and the effect that the game show host’s actions have. Instead, we look at the situation as it is when we come to make the choice. Two doors, one prize. 50-50 chance, right? Wrong. The host’s actions make switching a better bet. By throwing away one dud door from the two you didn’t choose initially, he’s essentially making it so that switching is like choosing between two doors and you win if the prize is behind either of them.
Taken from : Mind Hacks
