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Message: <blockquote data-quote="Sagiro" data-source="post: 1353769" data-attributes="member: 726">Ranger, orsal's explanation is correct, and he said it better than I was saying it.As to the riddle generally, here's my take:[spoiler]The way the original riddle in this thread is phrased is a very simple (yet obviously counterintuitive) example of conditional probability.  As stated, it presents you only with these facts:1. There are two children2. At least one of them is a boy.That's it.  That's all we know.  While we know there is an ordering to these children, we don't know anything about that ordering.  The boy could have been the first kid or the second kid, but we don't know which.  The riddle is the same as if we said:  "A woman has flipped two coins.  They've already landed but you're not allowed to look at them.  Then you find out that at least one coin landed heads.  Now, what are the odds that the other one is a tail?"I think all mathematically-inclined people here know that if you flip two coins, there are four equally-likely outcomes:1. HH2. TH3. HT4. TTIf someone now tells you that at least one coin came up heads, the only effect that has on the problem is that you can now eliminate "TT" as a possibility.  It doesn't make any of the remaining three outcomes any more or less likely.  (And of specific import, it doesn't make the HH outcome any more likely.) That leaves three equally-likely possibilities:1. HH2. TH3. HTNow you're allowed to look at the coins. If it turned out that the result was #1, then if you look at a coin that is heads, the other one is heads.If it turned out that the result was #2, then if you look at a coin that is heads, the other one is tails.If it turned out that the result was #3, then if you look at a coin that is heads, the other one is tails.Thus, in two out of the three cases, the other coin is a tails, or a girl in the original riddle.[/spoiler]-Sagiro</blockquote>

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