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Old 06-17-2012, 02:31 PM   #3
Steady Eddy
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Let's see... Suppose the 40% same from 4 successes in 10 trials. The 11th trial is a failure, we now have 4/11 = ..363636..., for a decrease of .03636...

Then, the 12th trial is a success, 5/12 = .41666... for an increase of .0530303...

It turns out that the decimal value of the 12th trial was larger than that of the 11th! This seems strange, b/c as the denominator grows, we'd expect the decimal value to shrink.

I think the answer to this paradox is that a positive outcome is not always equal to a negative one. For example, suppose I'm 1/100, a further failure to 1/101 is only a change of .00009901, but a successful trial yields a 2/101 which is a change of .0098.

BTW, positive changes aren't always larger than negative ones, the closer you are to 100%, the larger changes come from failures, but the closer you are to 0%, it's the other way around. Since 40% is closer to 0% than 100%, the absolute value of the success is larger, even though it has a greater denominator.
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