

The Monty Hall Problem - Would you switch to Door #2? - JacobIrwin
http://jacobirw.wordpress.com/2011/12/11/the-monty-hall-problem-explained/

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mv1
Umm, the correct answer is to switch doors. It has been discussed ad naseum as
you mention. The simplest way to see that the switch doors gives you a 2/3's
chance of winning is as follows.

Without loss of generality, assume that you always pick door 1.

If the car is placed randomly, you have a 1/3 chance of getting the car. To
see this, note that when not switching, you only win if your initial guess has
the car behind it, which happens 1/3 times.

When you switch doors you only win if not switching loses. Since not switching
wins 1/3 times, switching wins 2/3 times.

You can write a simple program to simulate the game and see that switching
wins 2/3 times.

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chromejs10
Wait so he's arguing that switching wont make a difference?

The host is guaranteed to open up one door that is a goat. So, instead of
thinking at the beginning that you have 1/3 chance of picking the car, instead
think that you have 2/3 chance of picking a goat. If you pick a goat and you
switch, then you win because the host HAS to show you the other goat. So think
about it that way: try to pick a goat and not the car at the beginning. That
is the simplest way I can explain why your chance of winning is 66% if you
switch when asked as opposed to staying with your original choice.

