(no subject)

[brooksmoses]

Jeff Atwood has just done a masterful bit of trolling, asking his readers a question of, "Let's say, hypothetically speaking, you met someone who told you they had two children, and one of them is a girl. What are the odds that person has a boy and a girl?"

As proof of the masterfulness of this troll, he now has about 750 comments on this post, which is about a factor of five higher than his usual. I can only assume this has been reddited and slashdotted and discussed in comments there as well. People have all sorts of answers, and they are by and large completely convinced of the irrefutable accuracy of their answer.

The actual numerical answer, of course, is 50% -- on the grounds that there are only a few meaningful probabilities in the real world. These are the once like 90% which means "pretty sure", 10% for "I doubt it", and in this case 50% which means "I have no clue one way or the other." (It does not, however, mean that this can be treated as equivalent to a coin flip for purposes of fair gambling.)

Jeff even alludes to this answer in his title of the post, calling it "The Problem of the Unfinished Game".

Consider that, in the information you're given, there is no mention of how you met this person.

If you assume a population of parents of two children of gender selected by probabilistic equivalent of a coin-flip (which nearly all of the respondents do, even though the actual distribution is not 50-50 and one ought to at least defend the assumption of non-correlation), and select all of the parents for whom one of the children is a girl -- let's say you meet parents on the street, and talk to each of them until you find one who meets this criterion -- you get an answer of 2/3.

If you assume the same population, and select a random girl and talk to her parent -- let's say you send your daughter to an all-girls age-segregated day-care, and talk to parents of other girls in the same class -- you get an answer of 1/2.

If you assume a population of parents of opposite-gendered kids -- and why shouldn't you? Maybe you're at a support group for them? -- then you get an answer of 100%.

Or, if you assume the real world, in which conversations that contain this particular bit of information but no information about the gender of the other child happen somewhat rarely, and their occurrence can be expected to have all sorts of correlations with the gender of the other child, and moreover you are selecting these people through some probably-not-entirely-random selection mechanism which Jeff has told you utterly nothing about -- who knows what you'll get?

(I think Jeff currently only has one kid, or I'd say the answer is "100% if Jeff has a daughter and a son, or 0% if he has two daughters.")

I somewhat despair of the implications of what it means that many people think that math alone can give them the answer to this question. Sigh. Grumble. Et cetera.

Comments

[xiphias.livejournal.com]

Um. If someone told me that they had two children, and one of them was a girl, then I'd go by their personality.

If they were a devotee of logic puzzles, or a mathematician, I'd figure that it was a 50-50 shot.

If a NORMAL person said, "I've got two kids and one of them is a girl," then it would mean that the other one was either a boy or intersexed or something like that. Because when NORMAL people say "one", they mean "exactly one," not "one or more."

[xiphias.livejournal.com]

(For purposes of record-keeping -- by this standard, I am not normal.)

[brooksmoses]

Hah! And, yes, exactly.

One is even making an assumption of whether the wording in the question means that they specifically said one of them is a girl, or if they said something that conveyed that data point in a different way (e.g., used a gendered pronoun or name for one of them).

[hitchhiker.livejournal.com]

i like that.

[rosefox]

It's an X!

[pantryslut.livejournal.com]

I have two children. One of them is a girl.

Thank you for making me giggle this afternoon. You can hear the stifled sounds in the background of this comment, yes?

[rosefox]

There's your answer, Brooks: 0%. *)

[brooksmoses]

And thank you, in return! I think your reply wins the internets.

[tenacious-snail.livejournal.com]

As a math question, it fails. As a how native English speakers regularly speak, it is unlikely that one would say this, unless the person has one girl and one non-girl. However, I can imagine that one could say "I have two children...my daughter, who is in Girl Scouts, spends her Fridays at the Foo" This does not mean that the other child is NOT a daughter, just that one is a Friday-Foo-going Girl Scout.

[tiger-spot.livejournal.com]

Hm. But people don't usually say "My daughter" unless they've only got one. They say "My older daughter" or "My daughter Jane" or whatever. So the exact phrasing of that sort of statement would be likely to be revealing. A name reference would be the most neutral about the other sibling's gender, I think.

[tenacious-snail.livejournal.com]

can you hear whether or not there is a comma between "daughter" and "is a girl scout"?

(though yes, I agree, usually when someone says "my daughter", they mean that they have one and only one daughter)

[tiger-spot.livejournal.com]

Hm. In that particular case, I would presume it had a comma whether I could hear it or not, because "My daughter who is in Girl Scouts" seems awkward as an identifying phrase.

[oneironaut.livejournal.com]

Or some other highly specific description -- 'I have two children, and the younger one, who is a Girl Scout ...'. That's still slightly unnatural to my ear, actually.

[xiphias.livejournal.com]

I just commented there that they're ignoring the possibility that the person is lying or deluded.

[johnpalmer.livejournal.com]

Or, if you assume the real world, in which conversations that contain this particular bit of information but no information about the gender of the other child happen somewhat rarely, and their occurrence can be expected to have all sorts of correlations with the gender of the other child, and moreover you are selecting these people through some probably-not-entirely-random selection mechanism which Jeff has told you utterly nothing about -- who knows what you'll get?

Chuckle. That was where my thoughts were going. How many parents say "I have two kids, and one is a girl" without intending to imply "and the other is, therefore, a boy"?

Well, clearly, there are smart-asses in the world, and other people who will make the statement with the desire to introduce ambiguity. But I'd bet the odds the parent has a boy and a girl is over 90%.

[green-knight.livejournal.com]

Ok, maths trolling aside, I expect the second child to be something unusual that defies normal descriptions. Most parents would say, on introduction, 'two girls' or 'a girl and a boy.' 'One of them is a girl' carries, for me, the unspoken, 'the other is... [slightly awkward silence] (a bloody nuisance/ tomboy/a freaking genius/thirteen going on thirty/not sure/has four legs/...)

"One is a girl, the other is also a girl' is either a misleading statement (the 'trolling' part above) or spoken by someone who is not very familiar with English, so for someone with two daughters *not* to say that outright, there has to be something very specific they want to say instead.

[heleninwales.livejournal.com]

When I first read the question, I assumed that one knew by some other means that one of the children was a girl. For example you and your daughter go out shopping meet one of her class-mates with her mum, who says something that leads one to conclude that there is another sibling.

I didn't do the assuming consciously, but my brain must have recognised that anything else didn't make sense. As you point out, the statement is just not what anyone would normally say. Unless they're either a bit peculiar or making a joke, such as, "We have two kids, one is a girl and the other is a very pampered poodle!"

[hopeforyou.livejournal.com]

But what if someone is born intersexed? What if they're transgendered and haven't determined what they are yet? I don't view gender as binary.

[hrj.livejournal.com]

For me, what turns this into an unanswerable question is the semantic bracketing ambiguity. It is completely unclear whether the information "one of them is a girl" is part of the parent's statement or is an abstract fact about the situation. Without clarification on that point, the anecdote doesn't convey enough meaningful information to evaluate the odds. In the first case, we evaluate it based on Gricean principles of cooperative communication. In the second case, we evaluate it based on statistical grounds.