Hacker News new | ask | show | jobs
by kgwgk 1035 days ago
>> I tell you I have two children and that I’ve just sent you an email with the sex of (at least) one of them, and ask you what you think is the probability that I have one boy and one girl.

> 1/2

So you say it's 1/2 even though you know that as soon as you read the message you will update it to 2/3. Is that right?

The message says that (at least) one of them is a girl or that (at least) one of them is a boy. In either case, you state that the correct probability is 2/3.

Why not say 2/3 already then?
1 comments
dragonwriter 1035 days ago
> So you say it's 1/2 even though you know that as soon as you read the message you will update it to 2/3. Is that right?

Nope, its 1/2 afterwards, too.

Because you knew you were going to get one, and that is additional information; for much the same reason as the scenario outlined after that in GGP, it is twice as likely that the one you would get whichever one you do get if it was not a mixed pair.

link
kgwgk 1035 days ago
I don't get it.

If I say that I have two children and (at least) one is a boy you will say that the probability that I have one boy and one girl is 2/3.

If I say that I have two children and (at least) one is a girl you will say that the probability that I have one boy and one girl is 2/3.

If I say that I have two children and (at least) one is a [unintelligible] will you say that the probability that I have one boy and one girl is 1/2 or 2/3?

Edit: If you're going to say that [unintelligible] could be anything other than boy or girl - and are not willing to assume that it has to be one or the other consider the following alternatives:

If I say that I have two children and (at least) one is a [word in a foreign language that you know that means girl or boy but you don't remember which one] will you say that the probability that I have one boy and one girl is 1/2 or 2/3?

If I say that I have two children and (at least) one is [of the same sex as the first child of some other person that you don't know] will you say that the probability that I have one boy and one girl is 1/2 or 2/3?

link