Author: John Merlino
Date: 15:32:30 01/08/02
Go up one level in this thread
On January 08, 2002 at 16:36:35, Scott Gasch wrote:
>The problem is easy to solve if you make a list of the possibilities:
>
>Key: Y = your choice, P = prize
>
> door
> 1 2 3
> I Y P
> II Y P
> III YP
>
>
>I. If you choose 1 the host will open 2. Switching to door 3 wins.
>II. If you choose 2 the host will open 1. Switching to door 3 wins.
>III. If you choose 3 the host will open 1 or 2. You switch and lose.
>
>So the only time switching is a bad idea is when you chose the right door
>originally. You have a 1/3 chance of guessing right originally. So if you
>switch when given the chance you have a 2/3 change of winning. If you stand pat
>then you still have a 1/3 chance of winning.
>
>And of course someone who walks in at the moment you are offered a switch has a
>1/2 chance of picking correctly unless you tell them your original choice and
>explain the situation.
>
>Of course the prize could also be under doors 1 or 2 (above)... but this is just
>a permuataion of the same chart.
>
>Scott
I actually wrote a very simple program to convince other people that this really
is true. Scott, you're on the right track here as to how to explain it to
somebody, so I'll just fill out your chart:
C = your choice
P = prize
door
I II III
1) C P -- Wrong initial choice, door II opened, switch, win
2) C P -- Wrong initial choice, door I opened, switch, win
3) CP -- Right initial choice, door I/II opened, switch, lose
4) C P -- Wrong initial choice, door III opened, switch, win
5) CP -- Right initial choice, door I/III opened, switch, lose
6) P C -- Wrong initial choice, door I opened, switch, win
7) CP -- Right initial choice, door II/III opened, switch, lose
8) P C -- Wrong initial choice, door III opened, switch, win
9) P C -- Wrong initial choice, door II opened, switch, win
So, you can see out of the nine possibilities, you win 1/3 of the time if you do
not switch, and 2/3 of the time if you do switch.
HOWEVER!.... Monty Hall was actually told about this problem, and he said it is
misnamed because that is NOT how the game actually worked (that would have been
too easy). There was NO GUARANTEE that a door would be opened, therefore, you
were not necessarily given the extra information needed to improve your chances.
jm
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