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

[Leyton Gull]

Well there's 2 kids. we know it's not too girls, so that leaves boy and boy or boy and girl. We know one is a boy so the other is either a boy or a girl, so it's pretty much 50% taking demographics etc into account. In the first was a girl we know it's not two boys so it's still 50%.

 

[hans kraay fan club]

Well there's 2 kids. we know it's not too girls, so that leaves boy and boy or boy and girl. We know one is a boy so the other is either a boy or a girl, so it's pretty much 50% taking demographics etc into account. In the first was a girl we know it's not two boys so it's still 50%.

If the question was worded as "A man has one male child. If he goes on to have another, what is the probability of it being male?" then absolutely, the answer is 50%.

That wasn't the question though.

 

[GT49er]

How?

A couple have two children. These events have four possible outcomes:

1. They have a boy and then a girl
2. They have a boy and then another boy
3. They have a girl and then a boy
4. They have a girl and then another girl

1 and 3 are two different outcomes. You can group them together as one 'result' but it is a result that has twice the likelihood of either of the others, so should be written as above.

Incorrect; you're starting from the point where they have no children - then, as you say, there are four possible combinations. But as they are starting with the boy already a fact, there are only two possibilities for the second child - boy or girl, 50/50. You can't turn the already existing boy into a girl to activate the other possibilities (well, these days I suppose you can, but let's not include that as part of these calculations!)

 

[Triggaaar]

Massive flaw in your thinking.

Nope.

Let's take your statements in turn:

"There is a 50% chance the first card is a boy" TRUE
"There is a 50% chance that the cards are the same gender" Also TRUE.

These statements are different ways of explaining the probability, they are not related to each other. Just look at one in isolation.

However 50% + 50% (in probability terms) equals 25%, ie one in four, as I said.

I'm willing to put a lot of money on it if you like

 

[Acker79]

If the question was worded as "A man has one male child. If he goes on to have another, what is the probability of it being male?" then absolutely, the answer is 50%.

That wasn't the question though.

Going with the idea that two children exist... We know one of them is a boy. We don't know if the first born was the boy referred to in the question, or the second born is. But we know one of them is a boy. So our options are:

boy first, then boy (.5x.5) = .25
boy first, then girl (.5x.5) = .25
girl, then boy second (.5x.5) = .25
boy, then boy second (.5x.5) = .25

Two of the four scenarios will result in the 'other child' also being a boy. .25+.25 = .5 or 50%.

 

[pastafarian]

How?

A couple have two children. These events have four possible outcomes:

1. They have a boy and then a girl
2. They have a boy and then another boy
3. They have a girl and then a boy
4. They have a girl and then another girl

1 and 3 are two different outcomes. You can group them together as one 'result' but it is a result that has twice the likelihood of either of the others, so should be written as above.

you have lost me
if you already have two children

boy and girl
girl and boy

are the same thing when you are talking about you already HAVE two children

if you said to a friend i HAVE two children.......a boy and a girl
you would consider him totally barking if he said phew that was lucky........you could have had a girl and a boy.

 

[hans kraay fan club]

Nope.

These statements are different ways of explaining the probability, they are not related to each other. Just look at one in isolation.

I'm willing to put a lot of money on it if you like

We are talking at cross purposes. You are answering (one interpretation) of the original question. I followed the path raised by the questions posed later in the thread about what the question posed meant - a different interpretation.

You won't accept it, I guess, but my answers are 100% correct of the interpretation of the question I chose
I'm fairly confident in the statistics course I studied at University.

 

[Acker79]

Unless this is a reference to a recent news story none of us are aware of about some parents embarcing their child's non-conforming gender identity...

 

[Triggaaar]

We are talking at cross purposes. You are answering (one interpretation) of the original question. I followed the path raised by the questions posed later in the thread about what the question posed meant - a different interpretation.

You won't accept it, I guess, but my answers are 100% correct of the interpretation of the question I chose

We can forget what the original question may or may not have meant for a minute, could you just clarify the exact question you are responding to?
EDIT - I can see it...

Will put in a separate post.

I'm fairly confident in the statistics course I studied at University.

I'm confident the years haven't been kind to you

 

[Fungus]

This is beginning to sound dangerously like the "Monty Hall problem".

Don't Google it.

Run away from NSC now!

 

[Diablo]

If you have two children, "ONE of them is a boy" the other one cannot be a boy otherwise the statement is false so there is 0% chance of the other being a boy.

 

[dazzer6666]

If you have two children, "ONE of them is a boy" the other one cannot be a boy otherwise the statement is false so there is 0% chance of the other being a boy.

....'and so is the other one'
....'the other is a man'

etc.

 

[Moshe Gariani]

We can forget what the original question may or may not have meant for a minute, could you just clarify the exact question you are responding to?

This.

There is a very clever clever explanation on the internet that apparently makes the answer to my question, or a subtly different question, 1/3 but I think it is all bollocks. I am firmly in Team 50%.

("Zero" is a possible but rubbish answer as it is not meant to be a trick question.)

 

[Triggaaar]

I think he means at least one of them is a boy. The question is effectively the probability he has two boys.

I agree with this interpretation of the question.

The answer to that question is 1 in 3 assuming the odds of a boy is 1/2 I.e ignoring identical twins and the fact 52% of babies are boys.

This is not correct.

Correct

No it's not. We know what we're debating here Hans, right?

Ignoring the possibility of it being a trick question, or there being identical twins etc, someone has two children, and we're being told that one is a boy, the chance of the other being a boy is 50% - but you disagree, right?

 

[hans kraay fan club]

This.

There is a very clever clever explanation on the internet that apparently makes the answer to my question, or a subtly different question, 1/3 but I think it is all bollocks. I am firmly in Team 50%.

("Zero" is a possible but rubbish answer as it is not meant to be a trick question.)

This is a little difficult to word, but basically:

"What is the probability of two children both being male, given the proviso that at least one definitely is?"

You have four possibilities (b/g, b/b, g/g, g/b), but the proviso allows you to rule out one of them.

If you think of it as heads and tails instead of boy girl, its perhaps easier to look at the raw probabilities / possibilities.

 

[Diablo]

This.

There is a very clever clever explanation on the internet that apparently makes the answer to my question, or a subtly different question, 1/3 but I think it is all bollocks. I am firmly in Team 50%.

("Zero" is a possible but rubbish answer as it is not meant to be a trick question.)

Did not think it was a trick question..but the fact is that if you have two children and you state "ONE of them is a boy"...you are saying also that the other one isn`t.

 

[Arthritic Toe]

If you have two children, "ONE of them is a boy" the other one cannot be a boy otherwise the statement is false so there is 0% chance of the other being a boy.

Blimey keep up. We've been there at post #15

 

[hans kraay fan club]

I agree with this interpretation of the question.

This is not correct.

No it's not. We know what we're debating here Hans, right?

Ignoring the possibility of it being a trick question, or there being identical twins etc, someone has two children, and we're being told that one is a boy, the chance of the other being a boy is 50% - but you disagree, right?

No - not at all. Read my posts #30, and #42. I've said the same as you - that the answer to that simple question is irrefutably 50%.

 

[Triggaaar]

No - not at all. Read my posts #30, and #42. I've said the same as you - that the answer to that simple question is irrefutably 50%.

30 doesn't say much, and 42 goes with the idea that he hasn't had the second yet.

I still think you're making a mistake with your other assumptions. Let's assume the question is this:

A man has 2 children, we don't yet know what the gender of either are. We toss a coin (heads we ask about his first child, tails we ask about his second child). We're told that the child (fist or second, doesn't matter) is a boy.

You think the chance of the other being a boy is 1 in 3? It's not, it's 1 in 2 (50%).

 

[hans kraay fan club]

It's 50% Do you disagree?

Yes