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<blockquote data-quote="2WS-Steve" data-source="post: 354022" data-attributes="member: 3289">Sorry, last post didn't get it quite right. This is the real reason case 1 is different from case 2, I promise!Let's say the guy has pictures of each of his two kids in his wallet; he shows the top picture to you.In case 1 these pictures are randomly arranged so we get these possibilities (top-bottom):M-MM-FF-MF-FIn case 2 the pictures also start out randomly arranged just like in case 1. However, since we specifically ask him to show us his son he rearranges the pictures if they're F-M. This gives us the following distribution:M-MM-FM-F F-FThe reason we can guess right more often in case two is because we're forcing the distribution to be less random.As you can see, the &quot;down card&quot; has a flat 75% chance of being female after forcing the rearrangement. Essentially case 2 is just a magic trick.</blockquote>

[QUOTE="2WS-Steve, post: 354022, member: 3289"] Sorry, last post didn't get it quite right. This is the real reason case 1 is different from case 2, I promise! Let's say the guy has pictures of each of his two kids in his wallet; he shows the top picture to you. In case 1 these pictures are randomly arranged so we get these possibilities (top-bottom): M-M M-F F-M F-F In case 2 the pictures also start out randomly arranged just like in case 1. However, since we specifically ask him to show us his son he rearranges the pictures if they're F-M. This gives us the following distribution: M-M M-F [B][I]M-F[/I][/B] F-F The reason we can guess right more often in case two is because we're forcing the distribution to be less random. As you can see, the "down card" has a flat 75% chance of being female after forcing the rearrangement. Essentially case 2 is just a magic trick. [/QUOTE]

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