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View Diary: Morning feature: The Monty Hall problem (with poll and statistics questions answered) (310 comments)

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  •  I'd like a link to the explanation (1+ / 0-)
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    plf515

    I'm at work and really don't have time to puzzle that one out.

    Hige sceal þe heardra, heorte þe cenre, mod sceal þe mare, þe ure mægen lytlað

    by milkbone on Tue May 05, 2009 at 07:55:59 AM PDT

    [ Parent ]

    •  OK (2+ / 0-)
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      plf515, milkbone

      The possible genders of her children in 1 are FF, FM, MF, MM.  The first one isn't possible, so the last three cases are left (and all equally likely).  In only one of those three cases are both children boys, so the odds are 1/3.

      In 2 the possible choices are only MM and MF since you know the first one is M, so it's 1/2.

      Yes, there are progressives in the rural South. 50 States.

      by Racht on Tue May 05, 2009 at 08:14:06 AM PDT

      [ Parent ]

    •  If she has two children... (2+ / 0-)
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      plf515, milkbone

      ...there are four possible arrangements of the genders: GG, GB, BG, BB (G=girl, B=boy).  If one of them is a boy, GG is excluded as a possibility, leaving 3.  Of those, only one is two boys.

      The second part (eldest is boy, what's second), is equivalent to a stand alone consideration of the second child, where there is a 50% chance of each.

      •  Interesting (2+ / 0-)
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        plf515, NCrissieB

        Obviously this is correct; the logic works. I'm still trying to puzzle out exactly how the substitution of eldest for one makes the logical difference, though. It just doesn't seem to be enough information to make that difference.

        Hige sceal þe heardra, heorte þe cenre, mod sceal þe mare, þe ure mægen lytlað

        by milkbone on Tue May 05, 2009 at 09:21:29 AM PDT

        [ Parent ]

        •  The sample spaces are different (1+ / 0-)
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          NCrissieB

          There are 4 combinations, listing elder and younger

          BB
          BG
          GB
          GG

          now, if we are told "the eldest is a boy" that leaves
          two combinations

          BB and BG

          if we are told "one of them is a boy" then there are
          three combinations:
          BB
          BG
          GB

          •  Depends on how you read it. (2+ / 0-)
            Recommended by:
            plf515, milkbone

            There are eight possible combinations for the three binary variables: "two children," "each is a boy or a girl," and "sex of child is known or unknown":

            {Bb, bB, Bg, bG, Gb, gB, Gg, gG}

            I used a simpler notation than in my other comment below: the children are listed in birth order, and the Capital means the sex is known.  Of these we can eliminate those with a capital-G, because there the known child is a girl, and the problem states "one of them is a boy."  So the known child is a boy and we're down four combinations:

            {Bb, bB, Bg, gB}

            In plain language this translates to:

            1. The older child (whose sex is known) is a boy, and the younger child (whose sex is unknown) is also a boy.
            1. The younger child (whose sex is known) is a boy, and the older child (whose sex is unknown) is also a boy.
            1. The older child (whose sex is known) is a boy, and the younger child (whose sex is unknown) is a girl.
            1. The younger child (whose sex is known) is a boy, and the older child (whose sex is unknown) is a girl.

            Of those four, there are two where the other child is a boy (older and younger), and two where the other child is a girl (older and younger).  So it's a 50/50 guess on the other child.

            The 'gotcha' answer equivocates on birth order.  It ignores birth order where the sibling is a brother (boy-boy), but distinguishes birth order where the sibling is a sister (boy-girl, girl-boy).

            If you know "the older child is a boy," we can eliminate six of the eight original combinations, leaving only: {Bb, Bg}.  Again, it's a 50/50 guess on the other child.

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