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Subject:  Re: 5 Statistics Problems To Change Your View Date:  11/25/2012  9:24 PM
Author:  warrl Number:  409586 of 591799

2. (Vitali set) We can all agree, I think, that if we throw a dart at a dart board in a completely fair way -- so that all zones of the same size are equally likely to be hit -- then the probability of hitting any particular zone is proportional to the size of the zone.

Let us make a dartboard which is a uniform tesselation of two shapes, one of them being one square inch and the other being three square inches.

Now let us put a powerful magnet behind each of the smaller shapes.

And let us throw at it a dart with an iron tip.

We have a dartboard where zones of the same size are equally likely to be hit, but zones of different sizes are hit in proportions which do not match their area.
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