Re: [Phys-l] Never Trust a Theoretician! - Monty Hall Revisited.

[Paul Nord <Paul.Nord@valpo.edu>]

The answer is 2/3 probability if you switch.

Imagine the game this way:
	You: Monty, I would like to choose both doors #2 AND #3.  I want you to give me the best prize that's behind either of those doors.
	Monty: I'm sorry but you have to pick just one door.
	You: I could play by your rules.  But let me tell you ahead of time that I'm going to choose door #1.  And then you will show me that either door 2 or 3 is a non-winner.  At that time I will switch my choice to the the other door -- the best of doors #2 and #3.

Or extend the game to 100 doors with only one prize.  You choose a door and Monty can always reveal 98 non-winning doors.  (Better yet, picture playing Minesweeper on a 10x10 grid with one mine.  You pick a square.  I show you 98 squares with no mine.)  The odds of winning by not switching are 1/100.  But when you switch you get the best choice of all of the other 99 doors - 99/100.

Paul


On Nov 23, 2011, at 10:12 PM, brian whatcott wrote:

> I seem to recall quite a protracted discussion here on the merits of the 
> Monty Hall Paradox.
> This concluded that in the three door variant - with the empty door 
> revealed, I seem to
> recall that if you stuck, you rated a one in three chance of winning: 
> but if you swapped
>  your door choice after the third empty door was opened, your chances 
> rose to one in two.
>
> But tonight I saw a Mythbusters experiment, nicely done *, that made the 
> relative chances
> one in three for sticking, and TWO in three for swapping doors.
>
> Bah humbug!
>
> Brian W
> * Discovery Channel (HD) 9-10 pm CST. Wed Nov 23rd 2011
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l