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Puzzle: I have two children ...

Crispy said:
In the OP, can the state of Child 1 affect the state of Child 2? What information, in the OP as stated, prevents the 2nd child from being a tuesday boy? If nothing prevents Child 2 from being a tuesday boy, then all possible children are possible. Half of all possible children are boys. The probability is 1/2. Add the "only" to the question in the OP, and you get the other answer.

two tuesday boys are allowed in the OP's question
Click to expand...
Irrelevant.

Three people have listed all the possibilities on this thread. All you have to do is go and check that they made their grid up correctly and counted the cells correctly.
 
ymu said:
Thing is, the correct answer is very well known, and it's not the one you're giving us. You might want to stop and wonder why that is rather than just repeating that you're right.
Click to expand...
I have never seen this problem before. If you are right and this is generally considered to be the correct answer, I may have to set out why it isn't properly and send it to someone.

Seriously.
 
littlebabyjesus said:
Yes. And to answer the objection that everyone seems to be getting wrong, the order of Child1/child2 is fixed by the declaration of one of the children. That is the order: declared; undeclared, as your knowledge stands at the point of working out the probability.
Click to expand...
No. The order is irrelevant except in so far as it helps us enumerate all the possibilities. You've decided not to do it the easy way and hence have buggered up your counting.

Instead of repeating the wrong answer again, why not go and look it up? There's a perfectly good explanation linked to in the OP.
 
Crispy said:
In the OP, can the state of Child 1 affect the state of Child 2? What information, in the OP as stated, prevents the 2nd child from being a tuesday boy? If nothing prevents Child 2 from being a tuesday boy, then all possible children are possible. Half of all possible children are boys. The probability is 1/2. Add the "only" to the question in the OP, and you get the other answer.

two tuesday boys are allowed in the OP's question
Click to expand...

this still gives 13/27
 
ymu said:
No. The order is irrelevant except in so far as it helps us enumerate all the possibilities. You've decided not to do it the easy way and hence have buggered up your counting.

Instead of repeating the wrong answer again, why not go and look it up? There's a perfectly good explanation linked to in the OP.
Click to expand...

I love ymu :cool:
 
ymu said:
No. The order is irrelevant except in so far as it helps us enumerate all the possibilities. You've decided not to do it the easy way and hence have buggered up your counting.

Instead of repeating the wrong answer again, why not go and look it up? There's a perfectly good explanation linked to in the OP.
Click to expand...
It's wrong.

Ok, one last go.

State of your knowledge at point of question:

there are two children

one is boy born on Tuesday (take this child out, whichever position he's in)


You are left with just one child at the point of consideration. This isn't a question about two children. It's a question about one child.
 
Think about it this way.

You have one child. It is a Tuesday Boy.

You get pregnant. Does the gender or birthday of your first child affect those of your second child? No.


You have one child. It is any gender/birthday you want.

You get pregnant. Is there any increased likelyhood of this child being a Tuesday Boy? No.

The variables are independent. This is not a drawing marbles from the bag question. Put only in the OP, and then you get the interesting, counter-intuitive answer.
 
You. Are. Wrong.

No matter what the second child is, for both to be boys the first one has to be a boy as well. Therefore you have to consider all possible combinations that could have given you this result. There are 13 of these, from a possible 27.
 
Reducing the problem to its simplest form, the possible combinations are:

BB
BG
GB
GG

We already ignore GG because the first child to be declared is a boy. lbj, you are arbitrarily discounting GB, thereby skewing the probability.
 
littlebabyjesus said:
It's wrong.

Ok, one last go.

State of your knowledge at point of question:

there are two children

one is boy born on Tuesday (take this child out, whichever position he's in)


You are left with just one child at the point of consideration. This isn't a question about two children. It's a question about one child.
Click to expand...
No, it's a Bayesian probability question and the information you are given very much affects the answer.

If I know nothing except that the family has two children, then all I know is that 1/4 of the time it will be two boys, 1/4 of the time it will be two girls and half the time it will be a boy and a girl.

If you then tell me that one child is a boy, I know it cannot be two girls. There are only two possibilities left, and one of them is twice as likely as the other one. The probability of a second boy is 1/3.

Now do the same thing with a boy born on a Tuesday and a sibling who could have been born on any day of the week, and you will get the correct answer.
 
ymu said:
If you then tell me that one child is a boy, I know it cannot be two girls. There are only two possibilities left, and one of them is twice as likely as the other one. The probability of a second boy is 1/3.
Click to expand...
Please think about the absurdity of what you have just written here.
 
Crispy said:
Put only in the OP, and then you get the interesting, counter-intuitive answer.
Click to expand...

If only one of the boys can be born on a Tuesday the answer is 6/13

B(Tue), B(Mon)
B(Tue), B(Wed)
B(Tue), B(Thu)
B(Tue), B(Fri)
B(Tue), B(Sat)
B(Tue), B(sun)

B(Mon), B(Tue)
B(Wed), B(Tue)
B(Thu), B(Tue)
B(Fri), B(Tue)
B(Sat), B(Tue)
B(Sun), B(Tue)

B(Tue), G(Mon)
B(Tue), G(Tue)
B(Tue), G(Wed)
B(Tue), G(Thu)
B(Tue), G(Fri)
B(Tue), G(Sat)
B(Tue), G(sun)

G(Mon), B(Tue)
G(Tue), B(Tue)
G(Wed), B(Tue)
G(Thu), B(Tue)
G(Fri), B(Tue)
G(Sat), B(Tue)
B(Sun), B(Tue)
 
If you get a load of families whose first son is born on a Tuesday, and then ask them the sex of their second child, and it will be 50/50 girl/boy. This is NOT that situation.
 
Crispy said:
Think about it this way.

You have one child. It is a Tuesday Boy.

You get pregnant. Does the gender or birthday of your first child affect those of your second child? No.


You have one child. It is any gender/birthday you want.

You get pregnant. Is there any increased likelyhood of this child being a Tuesday Boy? No.

The variables are independent. This is not a drawing marbles from the bag question. Put only in the OP, and then you get the interesting, counter-intuitive answer.
Click to expand...
you're thinking about this the wrong way round
 
Crispy said:
Think about it this way.

You have one child. It is a Tuesday Boy.

You get pregnant. Does the gender or birthday of your first child affect those of your second child? No.


You have one child. It is any gender/birthday you want.

You get pregnant. Is there any increased likelyhood of this child being a Tuesday Boy? No.

The variables are independent. This is not a drawing marbles from the bag question. Put only in the OP, and then you get the interesting, counter-intuitive answer.
Click to expand...

The children are already born. We're not predicting the sex of the second child given that the first one was a boy (in which case, you would be correct), we're asking about the probability that both are boys given that one is a boy.
 
ymu said:
The children are already born. We're not predicting the sex of the second child given that the first one was a boy (in which case, you would be correct), we're asking about the probability that both are boys given that one is a boy.
Click to expand...
50/50

(as long as they are independent variables – as it happens, if your first child is a boy, you're slightly more likely to have a boy second child as well – to do with the levels of testosterone in the mother)
 
"One of the children is a Tuesday Boy. The other is a Boy" = Green
"One of the children is a Tuesday Boy. The other is a Girl" = Red


One Half
 

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