# re:Fun with Bayes' Theorem

From: Amara Graps (Amara.Graps@mpi-hd.mpg.de)
Date: Fri May 04 2001 - 06:09:09 MDT

From: Lee Corbin (lcorbin@ricochet.net):
>3. You're on the Monte Hall show, and there is a big prize
> behind one curtain, and junk prizes behind the other two
> curtains. You pick one of the three at random. Monte
> then opens one of the other curtains and shows you a
> junk prize, and asks if you still want to keep playing.
> You say, "Yes, but let me switch my choice to the other
> curtain!". Monte says, "That's weird," but allows the
> switch. What is the probability of your getting the big
> prize?

The Three Door Puzzle.

The answer is: Always switch choices and take the remaining door. It
has a 2/3 chance of concealing the prize while your original choice
has only a 1/3 chance.

The fact that the host purposely picks a junk-door is the whole
trick. If the host had not purposefully picked a junk-door (and he
didn't know what was behind it), the probability would be 1/2 that you
would get the prize.

Here's a more detailed explanation...

At the start, you have no information, and all the doors have
probability 1/3. Now, the host asks you a slightly different question:
"I'm going to give you further information about all the doors except
one. Which door do you not want to know any more about?" You choose
"The prize is not behind door two." Since door one still has the
original information, its probability remains 1/3. Door two has
dropped to zero; thus door three (with the additional information) has
odds of 2/3. (Credit to John Gregory at Cray Research for stating this
more detailed explanation on sci.math.num-anaysis in Summer 1995)

Amara

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Amara Graps               | Max-Planck-Institut fuer Kernphysik
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"Never fight an inanimate object." - P. J. O'Rourke
```

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