A man has two children. One of them is a boy.

[Arthritic Toe]

"One out of two"...... "One Boy out of two Children is as clear factually as it can be.......

It just isn't though, however much you bang your mallet.
"One is a boy" is ambigious. It can mean "Only one" or "at least one".

How about I say "You know what? I think Bobby will get one this weekend." Now suppose we win 3-0 with a BZ hatrick. Would you really claim I had been wrong? Fact is, he had got one, and then another and then another.

 

[hans kraay fan club]

I think it matters. This is why.

Easy part 1:
Let's consider 100 couples have a baby. Half have a boy, half have a girl.
Now let's consider they all have a second baby, half having a boy, half a girl.

Hopefully most of us would agree that 25% have 2 boys, 25% have 2 girls, and 50% have one of each.

Agreed

Easy part 2:
If I walked up to a random couple and said 'do you have a boy, yes or no?' and they said yes, then the chances of their other child being a boy would be 1 in 3 (because 75% of the couples would have said yes, and of those, 1 in 3 (25% of total) would have a second and 2 in 3 (50% of total) would have a girl.

this is pretty much exactly the logic behind my argument.

Difficult part:
A random couple was chosen from the 100, and a random gender was told to me.
Say we ran this test 100 times, and each couple was chosen once. For the 25 couples with 2 girls, I'd be told one was a girl. For the 25 with 2 boys I'd be told one was a boy. For the 50 couple with one of each, 25 times I'd be told one was a girl and 25 times I'd be told one was a boy.
So on 50 occasions I'd be told one was a boy. In 25 of those cases, the other would be a girl, and in 25 of those case one would be a boy.

It's 50%!

This logic I do not follow. Sorry.

 

[Triggaaar]

A man has two coins. He decides to spin both.

Question
"What is probability of both landing on heads"
Answer
25%. Only one of four possible outcomes is heads/heads.

Yep, but that's not the question. The question is, if I told you one was heads, what is the possibility both are, and it's 50%. Not straight forward, I grant you, but it is. The question is, why did I tell you one was heads? A lot of the time I could have said one is tails, but when both are heads I had to tell you one was heads. It would be very different if you had chosen to ask me if one was heads, and I had said yes - then it would be 1 in 3 of them both being heads, but that's not what happened, I volunteered the information, and you're not taking into account the fact I could have said one was tails.

 

[Moshe Gariani]

I think it matters. This is why.

Easy part 1:
Let's consider 100 couples have a baby. Half have a boy, half have a girl.
Now let's consider they all have a second baby, half having a boy, half a girl.

Hopefully most of us would agree that 25% have 2 boys, 25% have 2 girls, and 50% have one of each.

Easy part 2:
If I walked up to a random couple and said 'do you have a boy, yes or no?' and they said yes, then the chances of their other child being a boy would be 1 in 3 (because 75% of the couples would have said yes, and of those, 1 in 3 (25% of total) would have a second and 2 in 3 (50% of total) would have a girl.

But the point is, I didn't find out by walking up to one of the couples and asking a specific question. That's not what happened, so I can't make the same deductions.

But this is really obviously completely irrelevant to the original question. Nobody said anything about the man coming from a perfectly distributed sample of 100 couples.

FWIW, if there was any "trick" to this it was to suck in the "1/3" sophists. It simply is not justifiable on any reading of the actual question and is therefore a completely wrong answer.

 

[Diablo]

But in the original question we don't know the answer to either. We know that one is a boy, but not which one. Most are choosing to read it as 'there is a boy, what is the probability of THE OTHER being a boy', which is absolutely 50%. However the question doesn't say that. It says at least one is a boy. Either could be that one, which is why you can't 'combine' the two possible b+g outcomes.

"It says at least one is a boy" where does it say that ?..am I missing part of original statement.... "A man has two children. One of them is a boy". is what I have....

 

[Triggaaar]

This logic I do not follow. Sorry.

In the words of Darth Vader:
Apology accepted.

In the words of Yoda:
You must unlearn what you have learned.

 

[Triggaaar]

Nobody said anything about the man coming from a perfectly distributed sample of 100 couples.

But we're going with the basic understanding that about 50% of children are boys, and 50% girls, from a sample of several billion.

 

[Moshe Gariani]

Let's run with this.

Do you think (in general, rather than within the confines of this question), there is the SAME probability of a two-child family having two boys, as there is they'll end up with one of each?

I believe there is a 25% chance of two boys and a 50% chance of one of each. Is that right?

 

[Triggaaar]

This logic I do not follow. Sorry.

We did something similar in stats at uni - there's a bag with 3 coins in. One is 2 white sides, one has 2 black sides, and the other has 1 white side and 1 black side. You pull one out and one side is black - what's the probability of the other side being black?

 

[Moshe Gariani]

But we're going with the basic understanding that about 50% of children are boys, and 50% girls, from a sample of several billion.

Obviously, but how do the 100 couples come into it?

 

[Arthritic Toe]

"It says at least one is a boy" where does it say that ?..am I missing part of original statement.... "A man has two children. One of them is a boy". is what I have....

They moved on from that and redefined the question to remove the ambiguity.

 

[hans kraay fan club]

I believe there is a 25% chance of two boys and a 50% chance of one of each. Is that right?

Agreed. So of those families (i.e. all those with a boy), only 1 in 3 has a second boy.

that's the logic.

 

[Triggaaar]

I believe there is a 25% chance of two boys and a 50% chance of one of each. Is that right?

Yes.

Obviously, but how do the 100 couples come into it?

That was just a way of making a number to help people think about the problem.

For HKFC:

We could make it 4 couples if you like. One has 2 boys, one has 2 girls, two couples have one of each.

You ask a random couple to tell you the gender of one of their children. The couple says they have a boy.

There is a 50% chance their second child is also a boy.

If you ran the same test 4 times, on average 2 times the couple you chose would have said 'boy' and 2 times the couple you chose would say 'girl'.
Of the 2 times that the couple said 'boy', 1 time they would also have a girl, 1 time they would have 2 boys.

 

[hans kraay fan club]

We did something similar in stats at uni - there's a bag with 3 coins in. One is 2 white sides, one has 2 black sides, and the other has 1 white side and 1 black side. You pull one out and one side is black - what's the probability of the other side being black?

2 in 3. You've pulled out your black side. There is no probability involved in that - its happened. There are three possible coin faces you could be looking at. Two of them (the two sides of the B/B coin) have black on the reverse. the other (the black side of the B/W coin) does not.

 

[Diablo]

It just isn't though, however much you bang your mallet.
"One is a boy" is ambigious. It can mean "Only one" or "at least one".

How about I say "You know what? I think Bobby will get one this weekend." Now suppose we win 3-0 with a BZ hatrick. Would you really claim I had been wrong? Fact is, he had got one, and then another and then another.

Nothing ambiguous ..." two children, One is a boy" if true other child cannot be boy

If you say BZ will get one this weekend and he gets three you are wrong(fact).........however I believe you mean at least one which of course is different..

 

[hans kraay fan club]

For HKFC:

We could make it 4 couples if you like. One has 2 boys, one has 2 girls, two couples have one of each.

You ask a random couple to tell you the gender of one of their children. The couple says they have a boy.

There is a 50% chance their second child is also a boy.

Thank you for this. Might I run with it..?

Here are your 4 couples:

Couple 1: boy boy
Couple 2: boy girl
Couple 3: girl boy
Couple 4: girl girl

As per your experiment, I ask a random couple for the sex of one of their children, and they reply 'boy'. This is YOUR example. Because of this answer, couple 4 are now irrelevant. We can only be left with:

Couple 1: boy boy
Couple 2: boy girl
Couple 3: girl boy

So if couple 1 where the respondents, the answer is that the other child is a boy. For couple 2 it is a girl. For couple 3 it is a girl.

Only 1 in 3 of the couples in YOUR example (of those with at least one boy, as per the original question) have a second boy.



(and yes, I DO understand your logic that only half of the b/g couples may have answered 'b' - I just don't take that same premise from the original question)

 

[Triggaaar]

Difficult part:
A random couple was chosen from the 100, and a random gender was told to me.
Say we ran this test 100 times, and each couple was chosen once. For the 25 couples with 2 girls, I'd be told one was a girl. For the 25 with 2 boys I'd be told one was a boy. For the 50 couple with one of each, 25 times I'd be told one was a girl and 25 times I'd be told one was a boy.
So on 50 occasions I'd be told one was a boy. In 25 of those cases, the other would be a girl, and in 25 of those case one would be a boy.

It's 50%!

This logic I do not follow. Sorry.

Can you explain why you don't follow it - which is the first sentence that you don't agree with/follow?

EDIT - ignore this, I'll reply to your other post

 

[Triggaaar]

Thank you for this. Might I run with it..?

Be my guest.

Here are your 4 couples:

Couple 1: boy boy
Couple 2: boy girl
Couple 3: girl boy
Couple 4: girl girl

As per your experiment, I ask a random couple for the sex of one of their children, and they reply 'boy'. This is YOUR example.

Yep.

Because of this answer, couple 4 are now irrelevant.

Well we can pretend the other couple didn't exist, it would be the same.

We can only be left with:

Couple 1: boy boy
Couple 2: boy girl
Couple 3: girl boy

So if couple 1 where the respondents, the answer is that the other child is a boy. For couple 2 it is a girl. For couple 3 it is a girl.

Only 1 in 3 of the couples in YOUR example (of those with at least one boy, as per the original question) have a second boy.

This is where you are wrong.

Why did couple 2 tell me they had a boy, why didn't they say they had a girl.
Same goes for couple 3.

On average, one of those couples would have said they had a girl, so we'd be left with 2 couples, one having 2 boys and one having 1 of each.

 

[hans kraay fan club]

Be my guest.

Yep.

Well we can pretend the other couple didn't exist, it would be the same.
This is where you are wrong.

Why did couple 2 tell me they had a boy, why didn't they say they had a girl.
Same goes for couple 3.

On average, one of those couples would have said they had a girl, so we'd be left with 2 couples, one having 2 boys and one having 1 of each.

As per my reply above, I do NOT believe that is a premise / scenario you can take from the original question'. This was simply presented to us as fact, that (at least) one child was a boy. It is a fair assumption from that to calculate your probability based on all families that meet this criteria.

 

[Arthritic Toe]

If you say BZ will get one this weekend and he gets three you are wrong(fact)..........

No he did get one(fact). Then he got two more.