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Subject: Re: Nice riddle: extrapolate to make it evident

Author: Paolo Casaschi

Date: 07:21:07 01/09/02

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I had the same problem and I found that an EXCELLENT way
to convince people is to extrapolate.

So you tell your friend: let's doit now with 10 doors.
You pick one.
Then I'll open 8 out of the remaining 9 and you are offered
to switch. What would you do ?

Then you doit with 1000 doors, yuo pick one and I'll open
998 out f the remaining 999.

Then you doit with 1 million doors. You pick one.
Now, out of 1 million it is very likely that you did
not pick the right one, so if I open 999998 out of
999999 remaining what would you do ???

It is easy to show that, with N doors, the first pick
of your friend divided the set of doors in two groups,
the selected door (with probability 1/N of being the right
one) and the other (with probability (N-1)/N that one of
these is the right one).
The fact that I open N-2 doors DOES NOT ADD ANY ADDITIONAL
INFORMATION about the probability of the two sets above, because
in any case I will be able to open N-2 doors without the
price behind.

Usually the one million example works.
If it does not, play the game with one million doors,
one buck a shot and they will convince quickly (or
you get rich).

--Paolo







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