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## #1 2006-06-15 10:33:07

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

### Probability

Problem:
I pick two reals x and y. I show one of them to you randomly by tossing a fair coin. You have to tell me if the number you see is the larger or the smaller of the two. How do you do this so that for any choice of x and y, the probability that you are correct is strictly larger than .5?

Letter, number, arts and science
of living kinds, both are the eyes.

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## #2 2006-06-15 13:22:49

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Cheat

X'(y-Xβ)=0

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## #3 2006-06-15 14:05:18

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Probability

I believe the answer is supposed to be:

If the number given is greater than 0, say the other is less than it.  If the number given is less than 0, say that the other is greater than it.

However, I also believe this to be incorrect.  That is because:

Is the same "size" as:

For any real value a.  That is, there exists a 1-1 and onto mapping from one set to the other.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2006-06-15 15:46:49

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Probability

Woah, that's really neat Ricky!  I thought of the zero thing before I read yours, and then I was very interested by the sudden turn of events.  The old magic of infinity...

igloo myrtilles fourmis

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