[dba-Tech] The Three Doors Problem

On 26 Aug 2005 at 13:40, Lembit Soobik wrote:

> I think you make it too complicated.
> forget the history.

That's the flaw in your argument. You can't forget the history.

> at the end, what you have is two doors:
> one is the winning door
> just pick one.
> doesnt matter what you had picked before

Yes it does.

> doesnt matter whether you swap or not.

Yes it does.

> and you can write simulation programs till the cows come home

And if they are written correctly, they will give you the correct answer 
over enough trials.

> fact is you have one right and one wrong and have to pick one
> so you have 1 out of two chance thats all.
> 

Fact is, when you first picked you had three choices.

The odds are 1/3 you are right initially.  In that one case, switching is 
wrong.

In the 2/3 where you were wrong initially, changing will always give you 
the correct door. (Assuming the problem is stated correctly. As I said 
previous, you need to qualify it by saying "I open another door 
which I know contains a dead fish and show you the contents"  If you could 
open the money door by accident, it is a different situation.)
 
So in 1/3 cases you win by staying, in 2/3 cases you win by switching.

-- 
Stuart