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

[dazzer6666]

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

Need to define the question better - too many answers:

1). It's a trick question; men don't have children, women do.

2). Somewhere very close to 50/50.

3). Is there something nasty Jimmy Saville-like going on here?

This, or the answer could be zero -the man is also a 'boy', so the children must be girls

 

[symyjym]

A man has six children. One of them is a boy, and so is the other one, and the other one, and the other one, and the other one, and the other one.

What is the probability that no one would say this?

 

[Megazone]

Is the trick bit of the question the man rather than a women?

 

[Triggaaar]

Chances of the other child being an identical twin are approx. 3/100

I think it's less than 1%

 

[Triggaaar]

So it's impossible for someone ever to say "one of my children is a boy.... and so is the other one" ?

Or to be asked 'Is one of your children a boy?', and reply with 'Yes, they both are'.

 

[Triggaaar]

What is the probability that the other one is a boy?

Well I guess it's close to 50/50 that the other will be a male, but there's also the chance that he is older, and is no longer a boy.

 

[Acker79]

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

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.

How do you get to one in three? The chance of second hildren, monozygotic twins aside, being a particular gender is independent. of the gender of the first child.

Heads/Tails is 50:50, 1 in two. But just because you get heads on one toss, doesn't mean you have to get tails on the following one.

The chance of the second child being a particular gender is the same chance that your first one is that particular gender.



It also depends what country your are in. In 2014 the uk population was 50.7% female, in Qatar it is 26.3%.

 

[hans kraay fan club]

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

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.

Correct

If there are two children, there are four possibilies:
Boy Girl
Boy Boy
Girl Boy
Girl Girl

The probability of both being boys, given NO additional information, is just 1 in 4.

The probability of both being boys, in light of the statement that (at least) one is a boy, is 1 in 3 (as you can rule out the possibility of Girl Girl)

 

[Arthritic Toe]

So it's impossible for someone ever to say "one of my children is a boy.... and so is the other one" ?

Sure its possible to say it, but its also possible to say "only one of my children is a boy.... and so is the other one", but its a contradiction.

However, I'm just being argumentative. You are right. I concede the point.

 

[hans kraay fan club]

How do you get to one in three? The chance of second hildren, monozygotic twins aside, being a particular gender is independent. of the gender of the first child.

Heads/Tails is 50:50, 1 in two. But just because you get heads on one toss, doesn't mean you have to get tails on the following one.

The chance of the second child being a particular gender is the same chance that your first one is that particular gender.



It also depends what country your are in. In 2014 the uk population was 50.7% female, in Qatar it is 26.3%.

I answered exactly like that then deleted it, because I had missed his implied proviso (using the statement in the question as a fact)

"How would you deduce that the probability is 1/3. Establishing the fact that the first child is a boy, has no relevance to the probability of the second child also being so.

Roll a dice - you have exactly 50% chance of rolling an even number. Regardless of that outcome, if you roll it again, you will again have exactly 50% chance of rolling evens.

In fact if you'd just rolled evens six times in a row, the chance of rolling evens again is still 50%."

 

[Arthritic Toe]

I think he means at least one of them is a boy.

Thanks for your psychic insight.

 

[pastafarian]

Correct

If there are two children, there are four possibilies:
Boy Girl
Boy Boy
Girl Boy
Girl Girl

The probability of both being boys, given NO additional information, is just 1 in 4.

The probability of both being boys, in light of the statement that (at least) one is a boy, is 1 in 3 (as you can rule out the possibility of Girl Girl)

You have totally lost me here

 

[Acker79]

Correct

If there are two children, there are four possibilies:
Boy Girl
Boy Boy
Girl Boy
Girl Girl

The probability of both being boys, given NO additional information, is just 1 in 4.

The probability of both being boys, in light of the statement that (at least) one is a boy, is 1 in 3 (as you can rule out the possibility of Girl Girl)

Firstly, I think my last reply was working on the assumption the second has not been born.

Secondly, the question states one child is a boy, and is asking about the chances of the other also being a boy, so the only choices are:

Boy we know of, plus girl
Boy we know of, plus boy

 

[Arthritic Toe]

Firstly, I think my last reply was working on the assumption the second has not been born.

Secondly, the question states one child is a boy, and is asking about the chances of the other also being a boy, so the only choices are:

Boy we know of, plus girl
Boy we know of, plus boy

It's their own bloody fault. Should've used contraceptives.

 

[hans kraay fan club]

Firstly, I think my last reply was working on the assumption the second has not been born.

Secondly, the question states one child is a boy, and is asking about the chances of the other also being a boy, so the only choices are:

Boy we know of, plus girl
Boy we know of, plus boy

Both answers are 'correct' depending on the interpretation of the question.

 

[Triggaaar]

Correct

If there are two children, there are four possibilies:
Boy Girl
Boy Boy
Girl Boy
Girl Girl

The probability of both being boys, given NO additional information, is just 1 in 4.

The probability of both being boys, in light of the statement that (at least) one is a boy, is 1 in 3 (as you can rule out the possibility of Girl Girl)

Incorrect.

Firstly:
If the man had two children, and the gender of each was written on overturned cards, and we looked at one card and it said boy, then the chance of the other also being a boy is 50%. Using the 4 possibilities you listed, the easiest way to think of this is that before turning over a card there's a 50% chance that the siblings are of the same gender, and turning over 1 card does not change that possibility (regardless of whether the first is boy or girl).
Another way to think of it is that if the cards are in order of age (say as the 4 possibilities you've listed) then the first card is boy, meaning the 2 possibilities starting with girl are no longer possible.

Secondly, we're not talking about being given cards. The information given is just that 'one of them is a boy', and unless debating the use of English (ie, assuming it means one of his two children is a boy), that doesn't give any clue as to the gender of the other, except for the case of identical twins, or the possibility he lives in a country where they murder baby girls etc.

 

[hans kraay fan club]

You have totally lost me here

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.

 

[symyjym]

Incorrect.

Firstly:
If the man had two children, and the gender of each was written on overturned cards, and we looked at one card and it said boy, then the chance of the other also being a boy is 50%. Using the 4 possibilities you listed, the easiest way to think of this is that before turning over a card there's a 50% chance that the siblings are of the same gender, and turning over 1 card does not change that possibility (regardless of whether the first is boy or girl).
Another way to think of it is that if the cards are in order of age (say as the 4 possibilities you've listed) then the first card is boy, meaning the 2 possibilities starting with girl are no longer possible.

Secondly, we're not talking about being given cards. The information given is just that 'one of them is a boy', and unless debating the use of English (ie, assuming it means one of his two children is a boy), that doesn't give any clue as to the gender of the other, except for the case of identical twins, or the possibility he lives in a country where they murder baby girls etc.

As been pointed out by [MENTION=21401]pastafarian[/MENTION] the option Boy Girl or Girl Boy are in fact one and the same.

 

[symyjym]

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.

Come on, you can't wiggle out of this one

 

[hans kraay fan club]

Incorrect.

Firstly:
If the man had two children, and the gender of each was written on overturned cards, and we looked at one card and it said boy, then the chance of the other also being a boy is 50%. Using the 4 possibilities you listed, the easiest way to think of this is that before turning over a card there's a 50% chance that the siblings are of the same gender, and turning over 1 card does not change that possibility (regardless of whether the first is boy or girl).

Massive flaw in your thinking.

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.

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