Solution to the Three Doors and 1 Prize Problem..

This is a famous problem in probability called the Monty Hall problem.. For more info goto
http://en.wikipedia.org/wiki/Monty_Hall_problem

The answer is it is always better to switch ur choice to the other door.. Chance of winning doubles if u switch ur door.. The solution goes like this..

Suppose doors are numbered 1,2 and 3. Its clear tat u hav an equal probability of choosing any of the doors. Now suppose tat the prize is behind door 1 and the other 2 doors hav goats behind.

Suppose tat u will always switch ur choice when the gameshow host asks u..

If ur choice was door 2, the gameshow host will open up door 3 for u and show u a goat. So since the prize is behind door 1 u will win if u switch to door 1.

If u picked door 3, the gameshow host will open up door 2 for and show u a goat.. So u will win again if u switch ur choice to door 1..

Now suppose ur choice was door 1, the gameshow host will open any of door 2 or 3 for u. This time u will lose if u switch ur door..
So u hav a 2/3 chance of winning if u switch ur door..

Now suppose ur choice was never to switch..

if door 2 was ur choice, u will lose..
if door 3 was ur choice, u will lose again..
if u had picked door 1, u will win.
So u hav a 1/3 chance of winning if u dont switch..

So ur chance of winning doubles if u switch ur doors..
Hope its clear.. The wikipedia article has links to java applets tat demonstrates tat the solution is correct..