#### Comment Preferences

• ##### 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

[ 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.

[ 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

[ 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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