On Sep 30, 2010, at 7:56 PM, Joel N. Fischoff wrote:
> Here's the deal: I want to randomly generate a number between 3 and 10. Is
> it more probable that I will get a higher number if I generate the number
> directly (i.e. between one and ten, and ignoring if I get one or two), or
> if I generate it indirectly (by generating a number between one and eight
> and adding two). It seems more likely that the latter would generate
> higher numbers more probably, because the chance of generating any given
> number (between one and eight) is 12.5%, while the former is 10% even. Am
> I right, wrong, or it just doesn't make one bit of difference?
The distribution would be the same, but the efficiency of the 1:10
scheme is worse. While it looks like a 10% chance, remember that 20% of the
time the number will be discarded and a new number generated, with a 20% chance
that that will be discarded, etc.. The net result is that for each "accepted"
number, the odds will be 12.5% for each. You will have an 8.5% "do-over" rate,
which is why the 1:10 scheme is less efficient than the 3:10 scheme.
-- Ed Leafe
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