Puzzle: I have two children ...

[beesonthewhatnow]

They are logical, they're just counter-intuitive.

That's the phrase I was looking for

 

[innit]

plane still bloody takes off.

 

[beesonthewhatnow]

"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

You have B(Tue) B(Tue) twice. This is where you have gone wrong.

 

[Crispy]

Who do I write to about this?

I'm amazed to have found a problem such as this to which the received answer is so wrong.

I stand with you, brother

 

[innit]

"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

you've got BTue BTue in there twice - look at strung_out's diagram

 

[strung out]

"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

you've got B(tue) B(tue) twice

 

[ymu]

Please think about the absurdity of what you have just written here.

It's pretty basic probability theory. This is not about independent coin tosses - its about Bayes Theorem and how information changes the probability of an event occurring.

You really should spend some time reading the well known solution before going on. Just insisting that you are right is not sufficient legwork to overturn a theorem that has survived centuries of head-scratching students declaring it impossible.

 

[beesonthewhatnow]

I stand with you, brother

I'm amazed at you over this one

C'mon, look at the list you just posted, carefully.

 

[strung out]

my sister managed to work this out last night, and when i explained it to her, she just went 'well duh, we learned this in year 9'

 

[Santino]

Look, here are 100 families with two children.

You ask one of them to name the sex of one of their children. They say boy. You can now discount all the G/G families. There are 75 families left. Only 25 of them have a second boy. 50 of them have a girl. The chance of them having one girl and one boy is twice that of having two boys.

 

[Santino]

I stand with you, brother

This is worse than when Anakin Skywalker killed those children.

 

[Crispy]

You have B(Tue) B(Tue) twice. This is where you have gone wrong.

Ah, but it's not the same B(Tue) B(Tue) - they're two different children, after all.

 

[beesonthewhatnow]

Ah, but it's not the same B(Tue) B(Tue) - they're two different children, after all

You're making a basic error here mate.

 

[Santino]

Where is kabbes in our hour of need?

 

[innit]

Where is kabbes in our hour of need?

Wherever he is, I reckon a silent tear is running down his cheek.

 

[strung out]

Where is kabbes in our hour of need?

tbf, he did explain all of this yesterday

 

[ymu]

Ah, but it's not the same B(Tue) B(Tue) - they're two different children, after all.

Not when the only defining characteristics of the child are B and (Tue). You're double-counting cells in the grid.

 

[Santino]

Here's a thought: Who thinks that of all 2-children families who have at least one boy, half of them have two boys?

 

[littlebabyjesus]

"I have two children and one is a boy. What is the sex of the other."

The order is now fixed. One; other. The question is about the 'other' child.

P (two boys) now 50/50); P(one boy, one girl) 50/50; P (two girls) zero

BB
BG
GB
GG

I am told that one child is a boy. I pick one of the two children at random. What are the chances that the child I pick is a boy? 2/3

This is a question about 2 children.


But: I am told that one is a boy, and asked what is the sex of the other. That is a question about 1 child.

 

[ymu]

"I have two children and one is a boy. What is the sex of the other."

The order is now fixed. One; other. The question is about the 'other' child.

P (two boys) now 50/50); P(one boy, one girl) 50/50; P (two girls) zero

BB
BG
GB
GG

I am told that one child is a boy. I pick one of the two children at random. What are the chances that the child I pick is a boy? 2/3

This is a question about 2 children.


But: I am told that one is a boy, and asked what is the sex of the other. That is a question about 1 child.

No. You're answering the question "what is the probability that my second child will be a boy given that my first child was a boy?" Ignoring slight non-independence and different sex ratios, the answer to this is 50/50.

We're answering the question "what proportion of families which have two children and at least one son have two sons?" The answer to that is 1/3.

They're very different questions,and hence have very different answers. The second question is set as a brain-teaser precisely because it looks like the first question but isn't.

Plane takes off - really.

 

[strung out]

 

[innit]

"I have two children and one is a boy. What is the sex of the other."

The order is now fixed. One; other. The question is about the 'other' child.

P (two boys) now 50/50); P(one boy, one girl) 50/50; P (two girls) zero

BB
BG
GB
GG

I am told that one child is a boy. I pick one of the two children at random. What are the chances that the child I pick is a boy? 2/3

This is a question about 2 children.


But: I am told that one is a boy, and asked what is the sex of the other. That is a question about 1 child.

you are very confused.

 

[Crispy]

Here's a thought: Who thinks that of all 2-children families who have at least one boy, half of them have two boys?

This question is phrased in a different way to the OP.

EDIT - like what lbj says

 

[Santino]

 

[Santino]

This question is phrased in a different way to the OP.

I know, but it gets to the heart of what the issue is.

 

[littlebabyjesus]

I have 2 children. One is a boy. What is the probability that I have two boys?

Order: declared; undeclared

Possible combinations:

BB
BG
GB

P(GB) = 0
P(BB) = .5
P(BG) = .5

 

[Jazzz]

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.

okay, I think I can sort this out. Personally, I find the phrasing of the question somewhat undefined.

Take this version:

Person 1: "I have two children"
Person 2: "Is one of them a boy born on a Tuesday?"
Person 1: "yes"

What is the chance the other one is also a boy?

This is the problem that is being considered. If one was to consider, say, a possibility that the problem stater was just reeling off the sex and day of birth of his eldest child, or anything in which the information in the additional part is not totally random in a sense, then it breaks down and the problem is indeed different.

Hope that helps.

 

[littlebabyjesus]

edit

 

[beesonthewhatnow]

But: I am told that one is a boy, and asked what is the sex of the other

That is not the question in the OP, and is why you are wrong.

 

[Crispy]

Oh shit.

The second part is not "What is the probability that the other child is a boy" but "What is the probability you have two boys?"

That's where we went wrong, LBJ.

Plane crashes into the mountain. No survivors.