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	<title>Way of the Mind &#187; fallacies</title>
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		<title>The &quot;one in a million&quot; fallacy</title>
		<link>http://www.wayofthemind.org/2007/12/03/the-one-in-a-million-fallacy/</link>
		<comments>http://www.wayofthemind.org/2007/12/03/the-one-in-a-million-fallacy/#comments</comments>
		<pubDate>Mon, 03 Dec 2007 17:22:54 +0000</pubDate>
		<dc:creator>Pedro Timóteo</dc:creator>
				<category><![CDATA[logic]]></category>
		<category><![CDATA[fallacies]]></category>
		<category><![CDATA[random results]]></category>
		<category><![CDATA[statistics]]></category>

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		<description><![CDATA[This is the first of a couple of posts dealing with No Way&#8217;s comment on my previous post. This one doesn&#8217;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 [...]]]></description>
			<content:encoded><![CDATA[<p>This is the first of a couple of posts dealing with <a href="http://www.wayofthemind.org/2007/11/30/the-universe-exists-as-evidence-for-god/#comment-33810">No Way&#8217;s comment</a> on my <a href="http://www.wayofthemind.org/2007/11/30/the-universe-exists-as-evidence-for-god/">previous post</a>. This one doesn&#8217;t deal with religion / atheism at all, so it may be refreshing for a change. <img src='http://www.wayofthemind.org/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' />  The next one does, though.</p>
<p>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 <em>gambler&#8217;s fallacy</em>.</p>
<p>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.</p>
<p>If you roll two, the odds of getting &#8220;66&#8243; are 1 in 6&#215;6, or 1 in 36. The chances of getting &#8220;666&#8243; are 1 in 216. And so on.</p>
<p>If you roll <em>twenty</em> dice, the chances of getting all sixes, or &#8220;66666666666666666666&#8243;, are 1 in 3656158440062976. Virtually impossible, right? You&#8217;d virtually never, ever get all 20 sixes at a try, even if you spent the rest of your life throwing dice. A &#8220;random-looking&#8221; result such as &#8220;31423461534212543212&#8243; is <strong>much</strong> more likely, right?</p>
<p>Nope. &#8220;31423461534212543212&#8243;, or any other <em>particular</em> result, is <em><strong>exactly</strong></em> as likely as &#8220;66666666666666666666&#8243;. If you were betting on a result, it would make as much sense to bet on one as on the other.</p>
<p>The consequence of that is the following: <em>after</em> you get a randomly achieved result &#8212; <em>any result!</em> &#8212; you can then look at it and say that the odds of getting <em>that</em> result are fantastically small&#8230; so small that it &#8220;surely&#8221; took a miracle to have arrived at it! </p>
<p>The problem is that it works for <em>any</em> result whatsoever. Like in the previous example: roll 20 dice, and the odds of getting <em>that</em> exact result are, as I said, 1 in 3656158440062976. Sounds virtually impossible, right? Yet, you&#8217;ve just arrived at it&#8230; by pure chance.</p>
<p>The argument from design adds a variation to the above, though, but that&#8217;s a matter for the next post, since I promised that this one would be religion/atheism-free. <img src='http://www.wayofthemind.org/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
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