Author: Scott Gasch
Date: 13:36:35 01/08/02
Go up one level in this thread
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
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