75%

Well Semck, let's be specific here. In b), you state that at least one is a boy, but the question asks about "the second one." So let's specify whether "the second one" means the other child (not the one that we know is a boy), or the second in birth order. :-)

I'm going with (n-1)/2n where n is the size of the population. Approximately 50% for non-small values of n.

Ah, good point Mujus. Tricking someone by being ambiguous isn't particularly clever IMHO, but I'll admit that I missed the ambiguity.

Excellent question, Mujus. "The second one" means "the one we don't know," i.e., "the other one." In fact, it's a sufficiently important point that I should rewrite the question:

Suppose you know ONLY the following two facts about Mr. Jones and his family:

a) He has two children.
b) At least one of them is a boy.

Assuming equal sex distribution in society, what is the probability that the other one is a boy?

Okay, then I stick with my original answer.

Each child is independent of the other like coin tosses. So baring a genetic predisposition towards one sex or the other, 50/50.

This question is a classic, I've heard it before several times and it's still so interesting every time anyone brings it up.

Spoiler: http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

Anyway, the answer depends on how you interpret the problem, but there's no way to argue the probability that the other is a boy is greater than 50%.

Linearts, I would have preferred you not post a link to the solution -- there's a reason I asked people not to post if they knew the answer. : ) Please don't read before you've discussed it among yourselves, people.

I posted a *link* to the solution, not the solution itself. If you want to solve it yourself, you're free not to check the link.

Oh, crap. No, you're right, sorry. I got the "please don't post the answer" part but missed "please don't answer *or otherwise respond* in the first 22 posts" D=

The way I see it this is the key sentence ''Assuming equal sex distribution in society, what is the probability that the other one is a boy?'' This means that A) the fact that he has two children is an irrelevant factor as they presumably make up a tiny proportion of society. Same applies for B, it doesn't matter that one is a boy, this how no influence on the sex of the other child.

So unless I have completely missed something I would assume the probability that the other is a boy is simply 0.500. As the facts stated are irrelevant.

Suppose you know ONLY the following two facts about Mr. Jones and his family:

a) He has two children.
b) At least one of them is a boy.

Should this question be rephrased?

Assuming equal sex distribution in society, what is the probability that "Mr Jones has two boys". This is different question than the one posed by the OP.

I disagree, spyman. Given the hypotheses (a) and (b), the statement "the other one is a boy" is logically equivalent to "Mr. Jones has two boys." Therefore, of necessity their probabilities are the same.

Let's say that the size of the population is 100 and there is an even distribution of gender. 50 boys and 50 girls. We know one of his children is a boy. There are 99 other children, of which 49 are boys and 50 are girls. So the odds of his other child being a boy would be 49/99ths would it not?

So I'm now changing my answer to ((n/2)-1)/(n-1).

I'd say 50+%. The + is some unknown small number. Some men are more likely to have boys, some are more likely to have girls, and some are dead even. Since Mr. Jones has at least one boy, he's less likely to be in the "more likely to have girls" group (although not impossible). That gives a slight edge to another boy.

If that turns out to be an old wives' tale, then I guess that makes me an old wife.

Yes Semck83 I started thinking that too right after I posted.
In that case my answer is 2/3.

Interesting. Rationale?

This question makes my head spin...

But what ifbthe population is 101 - 51 girls and 50 boys or 51 boys and 50 girls. The odds could be less than 50% or exactly 50% in an odd population because you don't have a person of neuter sex (assuming binary gender here).

Suppose you know ONLY the following two facts about Mr. Jones and his family:

a) He has two children.
b) At least one of them is a boy.
c) He owns a dog named Fluffy
d) his wife is actually a blond although she dyes her hair red
e) he pretends to work really hard but in fact outsources his work to China without his boss knowing.

Assuming equal sex distribution in society, what is the probability that the second one is a boy?

A: 50%

@Draugnar, that isn't an even distribution. The problem stated an even distribution and therefore there have to be an even number of people of which exactly half are boys and half are girls.

As far as the 1/3 - 2/3 option. We don't know which boy is being shown in the BB relationships so it gets weighted twice still making it 50/50.

@TMOW, the difference between b and c/d/e is that b directly interacts with "Assuming equal sex distribution in society" while c/d/e do not.

The question "what is the probability both are boys" is 25%

the question "what is the probability one of them is a boy" is 50%, which seems to include the way semck originally phrased it, but not if you nitpick it.

I feel like that's probably where the paradox lies, the interpretation and the perspective of the question.

You all are making the assumption that this probability is occurring w/o replacement. We're talking about a population, not drawing from a deck of cards, so in my view, you're overcomplicating the probability. The other boy is simply included in the assumed 50/50 population, so his sexuality has no bearing on the probability for the other child.

By the way, I'm split on the whole "equal sex distribution" thing. On the one hand nerds having as much sex as jocks sounds good. On the other hand, ugos having as much sex as hoties gives one pause.

Assuming equal distribution in society doesn't definitively state that at that moment in time there is am even number of people. It implies that balance is roughly equal when there is an odd number and all it really does is show no predisposition to one sex or the other. So it is still 50/50 because we don't know whether his neighbor has two girls or a boy and a girl or what. Each is independent of the other so 50/50. An assumption is not an established fact. We have two established facts. Two kods and at least one is a boy. Do we take.into account Mr. Smith is male?

Semck83 I have to go out, so I'll have to get back to this question later but we already know for a fact that Mr Jones has one boy, which leave open two possibilities, one of which is a boy and one is a girl.

Consider the probabilities if we did not know the sex of any of his children:
1. Two boys
2. Two girls
3. One boy /One girl

In two of the scenarios out of three he has a boy. Hence 2/3.