When intuition and math probably look wrong

Re:When intuition and math probably look wrong by dododo on Tuesday June 29, 2010 @03:11PM (#1472406)

isn't this the same kind of "intuitive" reasoning that fails at simpson's paradox? http://en.wikipedia.org/wiki/Simpsons_paradox

conditioning upon more events can lead to a higher probability. p(boy = 2 | boy >= 1) < p(boy = 2 | boy >= 1, tuesday) (or more precisely, conditioning upon more events can yield a distribution with less entropy)

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Re:When intuition and math probably look wrong by bad_user on Tuesday June 29, 2010 @03:44PM (#1472518)

You know, the problem with that conditional probability is that the sex of the second child is in no way conditioned by the sex of the first child, so ...

  p(boy = 2 | boy >= 1) = p(any child = boy)

And this was the original problem that led them to the 33% probability.

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Re:When intuition and math probably look wrong by dododo on Wednesday June 30, 2010 @12:10PM (#1475292)

in the sample space i was intending, that would not be the case. i was imagining boy as a random variable that counts instances in an order tuple of genders (the underlying sample space).

you're right, without this explicit construction, it's problematic.

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