man with 2 children

Looking on google this specific problem hasn't shown up for a long time:

You know a guy who has two children. Someday you see him walking in the park with a girl which appears to be his daughter since she calls him daddy. What is the probability that his other child is also a girl?

Are you a thirder, a halver or some other minority?

Groetjes,

But it's in the FAQ.

Cheers,

He could have 'rented' her....

Is this question really addressed in the FAQ? There seems to be a difference between this one and the one about the probability of both children being female. It seems to me that the answer to this question is 50 percent; this is because knowing that a -particular- child is female gives more information than knowing that -at least one- of the children is female. To put it another way, if you know the first child is female, then your options are f/f or f/m (with equal probability, assuming male/female is equally likely), while if you only know that one of the children is female, your options are f/m, f/f, or m/f (again with equal probability). The 'odd' thing about the problem seems to be that by knowing more about the situation, we're less certain about the gender of the 'other' child (i.e. with less information, it seems like we can guess the genders of the children more accurately). This is however a fallacy, since we only know with 2/3 probability that the genders are m/f or f/m; if we also have to assign which child is a given gender, the probability of being correct falls to 1/3, which is inferior to the 1/2 we have in the situation where we know a particular child is female (due to the additional information).

On 9 Nov 2001 13:54:13 GMT, Bernard El-Hagin

Then read more carefully I thought for a long time too that this is what is in the FAQ. My father had introduced me to this problem in aproximately the wording I used above, applying the same reasoning as is in the FAQ which I assumed was true. Years later I got in some discussion here and I came to the conclusion that it had to be wrong.

What is the difference with this and the faq (or why isn't it) and what's the change now (not nescecarily different of course)?

Groetjes,

Well, assuming that boys and girls are born with equal probability, then the answer is 1/2.

Now, if you bumped into him alone in the park and he said 'At least one of my kids is a girl', then the answer is 2/3.

Isn't this a FAQ?

Fred Klein