From: jerryd@PROBLEM_WITH_INEWS_GATEWAY_FILE (Jerry Donovan)
Subject: Re: RAAARRGGHH!!!! not again!
Date: Tue, 26 Jan 1993 16:18:52 GMT
Reply-To: jerryd@hpgrla.gr.hp.com
Organization: Hewlett-Packard, Greeley Colorado
X-Newsreader: TIN [version 1.1.4 PL7]

: >Birth order? No one mentioned age here. The question was, that given one
: >girl, what are the chances of the other also being a girl. Given a uniform
: >distribution, that means for 1-child families, P(girl) = P(boy) = 0.5
: >Therefore, given that one child is a girl, the chance that the other child
: >is a boy, is 0.5, same as if it were a girl. Try this analogy, and you'll see
: >what's wrong with your answer.
: 
: >You are throwing 2 consecutive dice. The first one turns up a six. What is
: >the chance of the second also being a six. It's easy to see that because dice
: >have no memory, the chance is also 1/6. Now, following your line of reasoning,
: >there are 36 different ways to throw the dice. Because 1 six already has
: >been thrown this leaves 11 combinations, one of which is a double six.
: >So, according to you, you only have 1/11 chance of throwing a second six.
: >Clearly this is dead wrong.
: 
: >--Ralph
: Ralph, you are dead wrong. Let's look closer at your dice analogy to see why.
: To compare the dice problem to the boy/girl problem, you need to toss the
: dice a bunch of times and write the results down and put them in a hat.
: This is because the two children are already born, and we're not saying
: that if a woman has given birth to a girl, and is pregnant, what is the
: probability that the next child is a girl. We're saying that both children
: have been born and you see one of them on the street, you don't know which
: child). You see a girl, what's the probability the other is a girl. 
: 
: Back to the dice... Roll two dice 100 times. Get 100 pieces of paper and
: write the results of the first die on one side and write the results
: of the second die on the other side of the piece of paper. Put all the
: pieces of paper in a hat. Now pick a piece of paper out of the hat.
: You see a six on the piece of paper, what is the probability that the
: other side has a six? IT IS 1/11!!!!!!! 

If you assume that birth order is important, and add the fact that you don't
know which child was born first, I'd agree with you.  But birth order isn't
mentioned in the puzzle.  You do know the order you see the child, so the
first child seen is the first child, and the unknown child is the second
one.  With this view, the answer is one-half.  If you assume birth order
is important then the answer is one-third.  Those answering one-third have
read more into the puzzle than was written.

As for dice, roll two dice without looking (under a box or something). 
Pull out a die.  It doesn't matter which die came to rest first or 
even was rolled first.  You see a six.  What are the odds that the other is 
a six?  (1/6)  This simulation more closely reflects the question posed this 
time.  If the question was that one of the dice was a six, what's the other
one, then the answer is different, namely the one mentioned above.

(More of a puzzle in poor english and miscommunication than probabilities.)

Jerry Donovan
I wonder what the person doing the FAQ is going to put in there.