Sunday, October 04, 2009

Monty Hall Answer

Sure, this has been done before. I just thought i'd write up my answer for this problem. I will assume you have read what the problem is already.

There are only two possibilities behind the door you pick: either a car or a goat. The probabilities for each are 1/3 for a car and 2/3 for a goat (before you do any switching etc).

Let us consider the first case, with the car behind the door you pick. Now the GSH reveals a goat. In this case, since the other, unrevealed door is also a goat, it would be best to not switch. Therefore, in the 1/3 case that you do have the car, you should not switch.

The other case would be if you had a goat. The GSH will unveil another goat. The unrevealed door now contains a car. In this case, you should switch, in order to obtain a car. However, the chance that this case is the one you have is 2/3.

This means that, overall, switching will be beneficial, since 2/3 times switching will will allow you to win.

I found this way of thinking through a little easier than the methods on Wikipedia. I'm not sure why. I hope my explanation is not wrong.

1 comment:

hungy said...

Intriguing. I didn't get it until i read the 1000000 doors example on wiki though :\

But yes, very good. i get it now :)