The Old techInterview Forum - I differ with 3 door monty hall solution.

I differ with 3 door monty hall solution.

When Monty opens one of the doors to the goat the odds of winning increase from 1/3 to only 1/2, it doesn't matter whether you chose to switch or not.
There are two ways to reason:
1. The past has no impact on new probability. The new situation is there 2 doors, one favorable, one not. So odds are just 1/2.
2. There are 4 scenarios when Monty opens the door.
i. I picked the favorable, Monty opens 1st unfavorable
ii. I picked the favorable, Monty opens 2nd unfavorable
iii. I picked 1st unfavorable, Monty opens 2nd unfavorable
iv. I picked 2nd unfavorable, Monty opens 1st unfavorable
So my favorable odds are 2/4 = 1/2.

yvcb
Friday, December 20, 2002

Do a google search for "monty hall problem". I'm sure you'll find enough explanations to satisfy you why the answer given is actually correct.

mhp
Friday, December 27, 2002

yycb

The _specific_ problem with your reasoning (2) above is that the four scenarios are not equally likely. Scenarios iii and iv have a 1/3 chance of ocurring, and scenarios i and ii have a 1/6 chance.

David Clayworth
Monday, January 06, 2003