Sunday, May 18, 2008


The key is we need to understand that the host knows where the car is. Ben picks door number 1, so at that point he has a 33.3% of being correct (so odds are against him because he has a 66.6% chance of being wrong). The host knows whether he is right or wrong, but he reveals one of the doors that was definately wrong (door 3).

Now it does seem like regardless to what the movie said there is a 50% chance of him getting it correct now.

But remember, before door 3 was revealed there was a 66.6% (in favor) that the car was in door 2 or 3. The host HAD to pick a wrong door out of 2 and 3, and since it is MOST LIKELY in either door 2 or 3 (before 3 was revealed), by eliminating door number 3 the chances are greater that is in door number 2 because ORIGINALLY the chances were better (66.6%) that it was in door 2 or 3.

If you still don't understand, look at it this way:

Bens pick - Door 1 (33.3%)
Other pick - Door 2 and 3 (66.6%)
Now say your a bystander, are you going to bet that Ben is right? or that its in either door 2 and 3?
Your going to go with the door 2 and 3 because chances are better. The host CANT REVEAL Ben's pick obviously, and the host CANT REVEAL the car, so he shows you that door number 3 doesn't have the car. So theres still a 66.6% chance that Ben's choice is wrong.

If the host didn't know what was behind the doors and randomly picked number 3 and it happened to be a goat, then yes he would have a 50% of being right. Totally different story.

I find it easiest if you just lay out all the different scenarios:
Assume Door 1 = Car, Door 2 = goat, Door 3 = goat

1. You choose Door 1. Host reveals Door 3 is a goat.
a) You stay with Door 1 = Win
b) You switch to Door 2 = Loose

2. You chose Door 2. Host reveals Door 3 is a goat.
a) You stay with Door 2 = Loose
b) You switch to Door 1= Win

3. You choose Door 3. Host reveals Door 2 is a goat
a) You stay with Door 3 = Loose
b) You switch to Door 1= Win

So, in switching you win 2 out of 3 times, while in staying with your original door you only win 1 out of 3 times. So, odds are in your favor if you switch.

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