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Subject:Re: Are you a "Mental Gymnast"? From:eric -dot- dunn -at- ca -dot- transport -dot- bombardier -dot- com To:"TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com> Date:Wed, 22 Jan 2003 12:20:51 -0500
<<The FAQ is not in error. Your chances of winning the prize are 1 in 3 if you
stick, 2 in 3 if you switch.>>
How can this be true?
Three doors:
A B C
Say the prize is behind A.
You Choose Monty Shows Stay Change
A B W L
C W L
B C L W
C B L W
Always staying with your choice or always changing simply results in 50/50 odds.
There are no other popssibilities in the above outcomes. Regardless of where the
prize is, there are only four posibilities.
1- You chose the winner, stay and win.
2- You chose the winner, change and lose.
3- You chose a loser, change and win.
4- You chose a loser, stay and lose.
4 posibilities, changing does not increase you chances. If you always change
your chances are 2:4 for winning or 50/50. If you always stay your chances are
2:4 for winning or 50/50. If you randomly choose one of the remaining doors,
your chance is 1:2 or 50/50.
<<The best possible answer for an interviewee is "I've seen this before. I
didn't believe the answer at first, so I wrote a simulation program, which
demonstrates that you should switch doors.">>
The simulation is above. WHat did I get wrong if it's incorrect?
Eric L. Dunn
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