🚀 go-pugleaf

In article <C1GuHw.zuF@austin.ibm.com>, bmoore@sunfish.austin.ibm.com (Bryan Moore) writes:
> >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!!!!!!! 

The way you put it, you are still wrong. You are *given* the *fact* that
1 dice is a six. Your p[iece of paper has a six on 1 side. There are
left the combinations of 6-1, 6-2, 6-3, 6-4, 6-5, and 6-6. No other ones
possible, because you allready *know* there's 1 six. So the chance of
the other side being a six is 1/6. You make the mistake of making
a difference on which side of the paper the six is on. When you pick
a paper, and it has a 2 on it, you will also have to check the other
side to see if there's a six on it. The combination of 6-2 and 2-6 are
identical, because it is given that one of the two is six. 

Let's bring this back to the boy/girl problem. 
The (wrong) reasoning is that the possibilities are BG GB GG and BB.
But if you includeboth GB and BG, you should also include an extra
GG and BB, if you want to take birth order into account. Chances stay 
50/50.

This whole thing can be found in any statistical textbook, and is 
easy to understand when you realise that dice do not communicate. They
have no way of telling the other dice "Hey, I'm a six". They are 
independant entities.

--Ralph