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Puzzling

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    $\begingroup$ Nice and simple. I find enumerating the possibilities to be ugly, and this answer abstracts as much as it can. In both cases, the only thing we can say about the second ball is that it's not the first... Physically picking up the second ball after looking at the first is no different than picking it up along with the first. $\endgroup$ Commented Nov 11, 2014 at 21:57
  • $\begingroup$ I agree, this answer cuts directly to the heart of the problem and solves it in plain words, which is why I like it. I would prefer if the stated answer were 2/3 for the sake of exactness, rather than 66%. $\endgroup$ Commented Nov 11, 2014 at 21:59
  • $\begingroup$ The big difference is, by looking only at one of the balls, you eliminate some possibilities: By combinatorics you would have 50% chance of both being red. But the cases where you picked a blue ball are not as likely because the ball I looked at was not blue, so some cases are excluded and lower the chance of these combinations to 1/3 $\endgroup$ Commented Nov 12, 2014 at 9:47