Two children

small_unicorn

(A) I have 2 children. They aren't both boys. What is the probability that both children are girls ?
(B) An artist has 2 children. The older is a boy. What is the probability that both children are boys ?

from book "The Moscow puzzles" by Boris A. Kordemsky

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Ninja

**Posted:** Tue Nov 03, 2009 3:35 pm

$LaTeX$

A. There are 4 equally likely events, boy-boy, girl-girl, boy-girl, and girl-boy. Thus the probably of two girls is $\boxed{\frac{1}{3}}$ .

B. Going through what we did for A, gives $\boxed{\frac{1}{2}}$ ?

**Posted:** Tue Nov 03, 2009 3:39 pm

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pascal12 · Riemann Hypothesis Offline Joined: 18 Mar 2009 Posts: 256

I think this is a variant of the boy-girl paradox, right? http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

**Posted:** Wed Nov 04, 2009 5:10 pm

$LaTeX$

Yes, it is.

**Posted:** Wed Nov 04, 2009 5:23 pm

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steve123456

Isn't the answer to (a) 1/4 because there's a 1/2 chance the first child is a girl and a 1/2 chance the 2nd child is a girl, and 1/2*1/2 is 1/4.

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$LaTeX$

No, not really, that's what it would seem like, but remember that these are puzzles.

Read my first post in this topic. (Order does matter)

**Posted:** Wed Nov 04, 2009 5:54 pm

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XxaznlaziiboixX · New Member Offline Joined: 01 Nov 2009 Posts: 2

... for the first one it would be 100% because theyre both not boys then for the second it would be 50% because its either going to be a boy or a girl.

**Posted:** Wed Nov 04, 2009 6:14 pm

$LaTeX$

For number 1, it isn't 100%. He could have a boy and a girl... It is $\frac{1}{3}$ as previously explained.

**Posted:** Wed Nov 04, 2009 6:28 pm

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steve123456

Wow, I'm so stupid. I didn't read that both children couldn't be boys. SO STUPID!

**Posted:** Wed Nov 04, 2009 6:37 pm

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fire123 · New Member Offline Joined: 03 Nov 2009 Posts: 1

my answer for b) is 1/2 because the artist has two children and one has to be a

boy so the two possibilities are boy,boy or girl,boy

**Posted:** Wed Nov 11, 2009 8:06 am