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November 28

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Bayes Theorem Equation

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Looking at the equation for Bayes' Theorem.

Assume that

Now assume that a positive integer number X (between 1 and 1 million) is picked at random.

let be "X is divisible by 2"

and

let be "X is divisible by 4"

We have

Thus

Therefore if we pick a positive integer between 1 and 1 million at random, the number we pick will not be an even number.

This is of course WRONG! But I can't see where the mistake is.

You can have fun with this:

let be "George Bush is an American"
and
let be "George Bush is the president of the United States"

202.168.50.40 22:59, 28 November 2006 (UTC)[reply]

Hint. At some point, rather late in your derivation, you take a step of the form ab = ca = c/b. Then you conclude that c = 0 implies a = 0. But if you substitute c := 0 in the equation ab = c, it becomes ab = 0. You cannot conclude from there to a = 0.  --LambiamTalk 23:32, 28 November 2006 (UTC)[reply]