in the movie 21 he says the 3 door thing but how does he get 66.7 from choosing the other door?

Question

i get that if all three doors have 33.3 percent of winning, so he chooses the first door, then the guy takes out the third door, leaving the first and second. then the student changes his mind to door 2 because he somehow said that the odds of it being that door went up to 66.7 percent ? I took stats in high school and i can't see how he got this, Please someone help me with this talk all smart or whatever i'll understand it

Update:

baxter, dude your crazy good, yeah it makes sense. the extra 33.3 come from him choosing not to take the second door, so the so since he didn't choose door 2 the percent from the third door go over to it.

Justin H · Accepted Answer

I asked the same question and here's how I understand it. You know that when you choose the first time that you had a 1/3 chance of being right and a 2/3 chance of being wrong. Once one of the empty doors is revealed, you're basically trading in that 1/3 chance you were right for the 2/3 chance you were wrong. 

http://answers.yahoo.com/question/index;_ylt=AoQRwpZKuZy27qjS_RryKX_ty6IX;_ylv=3?qid=20080330030126AAYeCFi

Baxter · Answer

This is confusing. I'll try to simplify it.


If there are 3 doors, and behind one is the prize, you picked door #1.

When the guy takes away the third door, that means he DID NOT take away the second door. This is the key.
He could have taken away the second door, but he chose the third instead. That means that the second door becomes more likely that it has the prize instead of the third, because the guy chose to take away the third door instead of the second, because the second MIGHT have the prize behind it.
So, that is what makes the odds better for the second rather than the first.

Hope you get it now. It is a bit hard.

Anonymous · Answer

First of to prove Baxter wrong 
(no offense)

If you think like that you forget that the car could ALSO be behind door #1, which makes it equally (more)possible that the car is behind #1 as behind #2. Ergo 50/50
This is still wrong though, it is as you first said: door #2 is more likely to contain the car.

Let me explain:

When the student first chose one out of three doors he has 33% chance of choosing the prize.
When the teacher then chooses door three, he also have a 33% chance of choosing the car (the teacher knowing which one is the car has nothing to do with probability, wich was the whole point in the movie..)

BUT, here's the interesting development: The teacher can now chose one more door, leaving him with 2 doors to open and the student with one door...... starting to see it?

Then he basically asks the student "do you want to switch places with me?" and be the one to open 2 doors.(one already proved empty) And the teacher would then get the students one and only door, door #1 to open.

What would you have done?  :)
1 door or 2 doors to open?
33% chance or 67% chance?




Hope It helped "enano"
Peace from Sweden
"Blonde's on the outside"

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in the movie 21 he says the 3 door thing but how does he get 66.7 from choosing the other door?

3 Answers