The Monty Hall Problem - Would you switch to Door #2?(jacobirw.wordpress.com)
jacobirw.wordpress.com
The Monty Hall Problem - Would you switch to Door #2?
http://jacobirw.wordpress.com/2011/12/11/the-monty-hall-problem-explained/
3 comments
[deleted]
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.
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.
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.