Tag Archive for 'statistics'

The "one in a million" fallacy

This is the first of a couple of posts dealing with No Way’s comment on my previous post. This one doesn’t deal with religion / atheism at all, so it may be refreshing for a change. :) The next one does, though.

This one concerns this: the argument that the combination of conditions necessary for life is incredibly rare, so such a result could never happen by chance. This is, of course, logically flawed, and is related to the gambler’s fallacy.

Consider the following example: get a bunch of normal, 6-sided dice. Roll one; the odds of getting a six are, of course, 1 in 6.

If you roll two, the odds of getting “66″ are 1 in 6×6, or 1 in 36. The chances of getting “666″ are 1 in 216. And so on.

If you roll twenty dice, the chances of getting all sixes, or “66666666666666666666″, are 1 in 3656158440062976. Virtually impossible, right? You’d virtually never, ever get all 20 sixes at a try, even if you spent the rest of your life throwing dice. A “random-looking” result such as “31423461534212543212″ is much more likely, right?

Nope. “31423461534212543212″, or any other particular result, is exactly as likely as “66666666666666666666″. If you were betting on a result, it would make as much sense to bet on one as on the other.

The consequence of that is the following: after you get a randomly achieved result — any result! — you can then look at it and say that the odds of getting that result are fantastically small… so small that it “surely” took a miracle to have arrived at it!

The problem is that it works for any result whatsoever. Like in the previous example: roll 20 dice, and the odds of getting that exact result are, as I said, 1 in 3656158440062976. Sounds virtually impossible, right? Yet, you’ve just arrived at it… by pure chance.

The argument from design adds a variation to the above, though, but that’s a matter for the next post, since I promised that this one would be religion/atheism-free. :)




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Creative Commons Attribution-NonCommercial-NoDerivs 2.5 Portugal