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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7 Responses to “The "one in a million" fallacy”

  1. Ross says:

    There is a problem here Pedro. In No Way’s post, he is saying you need 66666666666666666666 to have life, and ALL other choices would not sustain life. So any other individual combination is just as unlikely as twenty 6’s, but since any result other than twenty 6’s (11111111111111111111, 11111111111111111112,…,66666666666666666665) result in no life, then it would seem that it is incredibly unlikely for it to come about by chance.

  2. Ross says:

    Just to draw a parallel. What if I, without fail, won every lottery in existence for a year? Sure, you could say “Well, the winning combination is just as likely to pick as any one of the losing combinations” but the fact is that there are A LOT of losing combinations and only one winning one. This does not dispute the fact that I won the lottery (I obviously won, unlikely or not) but it would raise suspicion as to whether I did so based on pure chance or not.

  3. There is a problem here Pedro. In No Way’s post, he is saying you need 66666666666666666666 to have life, and ALL other choices would not sustain life. So any other individual combination is just as unlikely as twenty 6’s, but since any result other than twenty 6’s (11111111111111111111, 11111111111111111112,…,66666666666666666665) result in no life, then it would seem that it is incredibly unlikely for it to come about by chance.

    Yes, that’s what I mentioned in the last paragraph. :) I didn’t want to mention it here because I wanted this post to be free of theological questions. I’ll address that on the next post.

  4. Ross says:

    Okay, look forward to seeing it!

    Also, glad to see some posts here again, I was afraid WotM was dead (and it is pretty much the only blog I check on a daily basis).

  5. [...] fallacy often used by creationists to argue that “life could never happen by chance”. Go and read it, then come back, and I’ll give you my take on [...]

  6. No Way says:

    Pedro, I look forward to seeing you deal with the theological issues in your next post. That is because Ross is correct. The combination that results in life is no more or less likely to happen randomly than any other single instance of another. However, it is MUCH LESS likely to occur than ANY of the others.

    In a criminal court of law this kind of probability would certainly be considered as PROOF of innocence or guilt. But, we are talking more along the lines of a civil court. In civil court the burden is a preponderance of the evidence. While it is certainly not proof, one can see how it could be considered evidence.

    Even with that we have only talked about the existence of life. We haven’t even touched on other characteristics such as apparent order, etc.

    Also, I thought all the people that support the “science” of evolution would be interested in this link:
    http://www.drdino.com/articles.php?spec=67&kws=250,000
    If you can provide emperical evidence for evolution you can win $250,000. Perhaps someone could at least provide a preponderance of the evidence but I have never even seen that.

    BTW, the posting that spawned this post sounded more like that of an agnostic than an atheist.

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