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Re: Are you a "Mental Gymnast"?

Subject: Re: Are you a "Mental Gymnast"?
From: David Purdue <dp18367 -at- iplanet -dot- com>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Thu, 23 Jan 2003 11:06:25 +1100




eric -dot- dunn -at- ca -dot- transport -dot- bombardier -dot- com wrote:


<<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

The simulation is above. WHat did I get wrong if it's incorrect?

You assume that all 4 branches have equal probability, that is what
you got wrong.

In fact, the only random choice (where a probability is introduced)
is in your choice of A, B or C - 1/3 probability of each. Only
if you choose A does Monty have to choose a door at random, so
he has a 1/2 probability of chooseing each door - laws of probability
say we multiply the probailities - so the total probabilities are

Branch 1 - 1/6
Branch 2 - 1/6
Branch 3 - 1/3
Branch 4 - 1/3

Which adds up to 1, so everything is hunky dory.

on Branch's 3 and 4 you win if you flip, threfore if you flip you
have a 2/3 chance of winning!

DavidP
--
David Purdue, Service Account Manager
Sun Microsystems Australia Pty Ltd
Ph: +61 3 9869 6412; Fax: +61 3 9869 6288; mailto:david -dot- purdue -at- sun -dot- com


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References:
Re: Are you a "Mental Gymnast"?: From: eric . dunn

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