Puzzle: I have two children ...

[kabbes]

This is bizarre. LBJ is telling me that I am wrong and then writing the exact same thing that I wrote.

 

[strung out]

no, you're wrong

or i should say, you appear to be answering a different question to the one asked. where does it say anything about the first boy being locked into position one?

 

[littlebabyjesus]

OK, have I misunderstood?

What do you say is the answer to the Tuesday question?

 

[littlebabyjesus]

or i should say, you appear to be answering a different question to the one asked. where does it say anything about the first boy being locked into position one?

You now have a criterion for position one: the child whose sex has been declared.

The answer to the OP is 50/50.

 

[strung out]

13/27 is the correct answer to the tuesday question, unless you fix the tuesday boy into position one, in which case it's 50/50. the question says nothing about the boy being fixed in that position though.

 

[kabbes]

Bearing in mind that the question merely says that you know that one of the children is male and not which of the children the male child is, the probability of two males is 13/27.

 

[littlebabyjesus]

13/27 is the correct answer to the tuesday question, unless you fix the tuesday boy into position one, in which case it's 50/50. the question says nothing about the boy being fixed in that position though.

You fix him by declaring him.

The positions are:

1. Declared

2. Undeclared

This is the state of your current knowledge.

 

[kabbes]

You now have a criterion for position one: the child whose sex has been declared.

Where and why do we have that declaration? It's certainly not in the question.

 

[strung out]

why can't it be

1. Undeclared

2. Declared

?

 

[littlebabyjesus]

Bearing in mind that the question merely says that you know that one of the children is male and not which of the children the male child is, the probability of two males is 13/27.

One of the children will be declared.

The other will not.

You tell us information about the child to be declared. The act of declaring fixes that child's position.

 

[kabbes]

For the avoidance of doubt, and as I already said in what you quoted, lbj, if you know at the outset that the elder child is male then the probability that the younger child is also male is a simple 50/50.

 

[littlebabyjesus]

why can't it be

1. Undeclared

2. Declared

?

In reality, there are no numbers, simply the positions 'undeclared' and 'declared'

 

[littlebabyjesus]

For the avoidance of doubt, and as I already said in what you quoted, lbj, if you know at the outset that the elder child is male then the probability that the younger child is also male is a simple 50/50.

But I am saying that this is also the case when elder/younger is not stated.

 

[innit]

plane takes off

 

[kabbes]

You tell us information about the child to be declared. The act of declaring fixes that child's position.

Er, no it doesn't.

I have two cats. I declare that one of them is male and he was born on a Tuesday.

Have I told you anything at all about whether he is the older or the younger cat?

 

[Gromit]

Er, no it doesn't.

I have two cats. I declare that one of them is male and he was born on a Tuesday.

Have I told you anything at all about whether he is the older or the younger cat?

Are either of them in a box with poison gas and a decaying particle?

 

[Santino]

Let's do an empirical test. Everyone reading this thread: go and grab two children at random.

 

[kabbes]

I'm not declaring that either.

 

[littlebabyjesus]

Er, no it doesn't.

I have two cats. I declare that one of them is male and he was born on a Tuesday.

Have I told you anything at all about whether he is the older or the younger cat?

Forget older or younger.

For the sake of this discussion, there are four positions:

BB
BG
GB
GG

The order is fixed by the declaration of one: the declared child now becomes the first in each pair.

Therefore, declaring one child to be a boy leaves the probability that the second is a boy at 50/50.

 

[Santino]

What about black and white marbles in a bag?

 

[kabbes]

Forget older or younger.

For the sake of this discussion, there are four positions:

BB
BG
GB
GG

The order is fixed by the declaration of one: the declared child now becomes the first in each pair.

Therefore, declaring one child to be a boy leaves the probability that the second is a boy at 50/50.

Ah, you mean "without loss of generality, assume that the declared child is the first one."

 

[littlebabyjesus]

Ah, you mean "without loss of generality, assume that the declared child is the first one."

Nope. I mean that there is no first one until some information about them has been given. Once you have information about one but not the other, they are then given an order if you are only considering the information given.

The answer to the OP is also 50/50 by extension of the same principle.

 

[kabbes]

I think I may have squared the circle -- it depends on whether the declared child is picked at random or whether he is chosen by the parent specifically because he is a boy.

You need

P(both are boys given one is a boy)
= P(both are boys)/P(first declaration was a boy)

The probability of the first declaration is therefore crucial. And we aren't given information about that at all.

 

[The Boy]

plane takes off

bastard

 

[littlebabyjesus]

No, that makes no difference. The first child has been declared. The probability of first declaration was a boy is 1.

 

[kabbes]

Let's suppose that we have two completely random children. Then we're in the situation most of us have been describing.

On the other hand, if we have a parent of a pair of children and the parent has a rule that says that they must tell you that one child is a boy (or something similar), then the probability of the second child is 0.5, as lbj says.

 

[Gromit]

Its posed as a purely mathematical question but the ratio of male to female sperm should be factored in. A ratio which we are being led to believe is going further in favour of female due to environmental factors.

 

[kabbes]

No, that makes no difference. The first child has been declared. The probability of first declaration was a boy is 1.

Not if you've picked a pair of children randomly. There may not even have been a boy in the pair.

It's like Monty Hall.

 

[littlebabyjesus]

Not if you've picked a pair of children randomly. There may not even have been a boy in the pair.

It's like Monty Hall.

You have already been told (ie the probability is 1) that:

there are 2 children

one is a boy

(and in OP version: that boy born on a Tuesday)


This is the state of your knowledge.

 

[kabbes]

But I don't know whether the fact that one would be a boy is something that was inevitable or something that was random.