Given that there is at least one male, there are 3 possible birth orders: BB, BG, or GB, which all have equal probability. Thus, the answer is 1/3. Fact.

75%

This is no different than saying you flip two coins (this is where the even odds comes in) and that at least one is heads. What is the prob that the other is too. There are 4 possible outcomes, of which 3 include at least one head (HH, HT, TH)

... I don't know if I have thought this through properly, but my girlfriend is bugging me to take her shopping. I'll have to think about this later. That is my intuitive answer, but I probably haven't thought it through later.

There have been more than 22 posts, so I don't feel bad intervening to declare that uclabb, first among all the posters, is correct. Congratulations.

The answer is 1/3.

Typo... thought it through *properly

@spyman, but one boy/one girl is twice as likely as either two boys or two girls.

The fact that he already has a boy has no bearing on the answer.

@philcore, you indicating flipping two coins. Have you considered flipping one coin twice?

No it isn't. Because you don't know the order of the children either BG or GB is eliminated bringing ot back to 50/50. And you still have to take into account the father on the n/2... meaning you meed to rdduce the remainign male amd remaining total populace by 2.

@Draugnar, I believe you are reading more into "Assuming equal sex distribution in society" than I am. You are assuming it means "assuming equal odds of a child being born a boy or a girl" I took it for the pure meaning of the words used. Half the people are male and half are female of which population we are only able to view one and it is a boy. If we were able to observe that the neighbor had a girl then that would balancing things out.

wait, I want too change my answer, we're looking for the prob of both boys (or both heads in my coin analogy), the answer is then 25% because only one of the four possible outcomes is favorable.

Draug, you're not calculating a conditional probability. Even if you were, the total population of both genders is so massive that it would make no difference if you eliminated two males from the total.

No, you are voewing *two*. You forget the dad.

@alderain, the physics of twins is different than the physics of consecutive births, I would need synapse to explain that one to me before I could answer ;-)

@2WL - I actually agree. That is why I said 50/50. It is no different than a coin toss.

what im saying is that from the perspective of not knowing what either boy is, you have to say that there is a 50/50 chance that each individual kid is a boy. even if you know one of them is a boy, it doesn't really change that you don't know *which* one is, so you can't change the probability.

given a 50/50 chance for each, if you ask, whats the chance they both are, you have to say 25%.

so that's one way of looking at it, I believe.

but then if you just take it to mean that Kid A is a boy, so what is the probability that Kid B is a boy, it's 50%, obviously.

The analogous statement about a coin toss would be the following:

A fair coin is tossed twice. You know that at least one of the tosses resulted in heads. What is the probability that the other did, as well?

The answer would still be 1/3.

But philcore, one of your 4 possibilities is impossible so can't have a 25% chance.

Hrmm, so the 1/3 argument is as follows?

Assuming even distribution of boys and girls...
25% both boys
25% both girls
50% one boy and one girl

But in this case we know the 25% both girls option is out. So that leaves 25%/75% which is 1/3.

Hrmm.

wait why 1/3 enlighten a dumbass

Correct, Alderian.

Of all the families in the US with two children, a quarter have two boys, a quarter have two girls, and half have one of each. GG is out. Only a third of the rest are BB.

The two statements precisely sufficient to tell you that (a) we're in the universe of two-children families, and (b) GG is out.

1/3 of those families have BB.

how about i add a spanner to the works?

Do it.

whats to say the two children are not twins?

There's nothing to say that they are or aren't.

Still 50/50. We know 1 child ia a boy. If the first is a boy then 50/50 the second is and if the second is the boy then 50/50 the first is. That is why BB counts twice.

sorry irrelevant point just figured it out in my head, i still don't see how the either child being a boy changes the chance of the remainder child being 50/50

oh. weird

Draug, we don't know which child child 1 is, though. We only know "at least one child is a boy." That is a statement that is true about BB and BG families. We know nothing else to distinguish them.