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Re: Are you a "Mental Gymnast"?

Subject: Re: Are you a "Mental Gymnast"?
From: "Diane Evans" <diane_evans -at- hotmail -dot- com>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Tue, 21 Jan 2003 15:26:47 -0800


Pretend you are on a game show where you need to
choose between three doors to win a prize. Only one of
the doors hides a prize. The host of the show knows
which door has the prize, but you don?t.

After you choose a door, the host opens one of the
doors you did not choose. The door opened does not
have the prize behind it. Next the host gives you a
chance to change your mind. Assuming you want the
prize, should you change your mind?

And the correct answer (from your friendly resident mathematician):

The host knew what door the prize was behind. The first time you choose a door, you have a 1/3 chance of winning. The host opens a door, which you know is the wrong door (or he wouldn't have opened it). The chance that you picked the wrong door increases slightly, enough for you to change your mind.

Look at it this way: Suppose you had 100 doors to choose from. Your chance of getting it right is 1/100. The host opens 98 doors that he knows are empty. Are you going to change to the only door he hasn't opened? Definitely!

http://mathforum.org/dr.math/faq/faq.monty.hall.html



Diane Evans
Technical Writer

Washington State Coordinator, Tombstone Project
http://www.rootsweb.com/~cemetery/washing.html




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