A woman has two kids. One is a boy. What are the odds the other is a boy?

Choose whichever you think is closest.

50%, of course?

Or so you think.

Consider the four possibilities for having two children:

B/B
B/G
G/B
G/G

We can eliminate G/G because we know that one of them is a boy. This leaves B/B, B/G and G/B. Only 1 in 3 has the other as a boy also.

If you know one of the random factors, it's no longer random. Therefore, 50%, as there's only the possibility of being Boy/Girl, or Boy/Boy.

It's seriously not 50%.

Math is weird.

Or so you think.

Consider the four possibilities for having two children:

B/B
B/G
G/B
G/G

We can eliminate G/G because we know that one of them is a boy. This leaves B/B, B/G and G/B. Only 1 in 3 has the other as a boy also.

This only matters if the order in which they are born makes a difference, which it doesn't in this case. So I'm sticking with 50%

Why wouldn't birth order matter? It's a 33% chance for 2 boys.

G/B is not a possibility if the first one is a boy.

I never said the first one was a boy.

definitely 25%. 1/2 times 1/2 is 25%. Assuming there's nothing freaky going on with the genes that makes it less or more likely to get 2 boys in a row.

EDIT: Oops, didn't read that the boy isn't neccesarily the first one

definitely 25%. 1/2 times 1/2 is 25%. Assuming there's nothing freaky going on with the genes that makes it less or more likely to get 2 boys in a row.

We already know that one of them is a boy, which means it's not one half times one half.

Though yeah, you're right Opeth.

We have the following chances (as you said)

BB
BG
GB
GG

Now, stating that this woman has got two children, we know that all the different combinations above works. We assume 50% for both chances, in case anyone wonders. Now, we are given that one of the children is a boy. That eliminates GG, and leaves us with 3 different combinations. only one of them gives BB, thus BB = 1/3 in this case.

I don't like how these things are stated though. I mean, usually, I'd think "oh, the first one is a boy" when seeing "One is a boy. What are the odds the other one is a boy as well?"

Basically, when you know for sure one child is a boy, you can leave it out. However, when you know that one of the children is a boy, that's when you'll do stuff liek dis.

How can it be anything other than 50%? The child is either a boy or a girl...cant be anything else...unless the child is a hermaphrodite or sexless. The odds of having a girl after 15 boys is still 50%. Just like when you flip a coin...right?

The underlying factor here is if the order of the children matter.

B/B
B/G
G/B
G/G

If we were to look solely at the end result, we can consider bg and gb to be the same possibility, i.e. the results are only:

two boys
one boy and one girl
two girls

Possibility of two girls is ruled out thus only leaving the result to be either two boys or one boy and one girl. In this case, it would be 50-50.

If the order of it matters, the original topic says -nothing- about order until this post.

B/B
B/G
G/B
G/G

So your original post leaves a huge gray area leaving the possibility of both being 50% and 33.3(repeating)%. inb4Shrodinger's cat.

If order doesn't matter, it's either/or. 50%. How could it possibly be anything else?

Order does NOT matter, therefore it's a 33% chance for 2 boys.

It's 33%(Well, One third)
Put simply.
They have one boy. That eliminates one option.
B/G
G/B
B/B
G/G <- Cannot happen in this situation

Then we have 3 equally weighted options left, so they each have a third chance of happening, 2 options are B/G, and 1 is B/B, so 1/3 times on average, it will be 2 boys.

Order does NOT matter, therefore it's a 33% chance for 2 boys.

You didnt ask what the odds where for 2 boys, you asked, "What are the odds the other is a boy?". Its an independent event. The other child can only be a boy or a girl, so its a 50% chance "the other is a boy".

Isn't there a higher chance to give birth to a female to begin with?

Isn't there a higher chance to give birth to a female to begin with?

That is true. I believe out of every birth, 2/3 chance = female ; 1/3 chance = male, or something or the like. I don't remember the exact %. So if that's correct, 33% is the true answer.

That is true. I believe out of every birth, 2/3 chance = female ; 1/3 chance = male, or something or the like. I don't remember the exact %. So if that's correct, 33% is the true answer.

So there's about twice as many females on the planet compared to males?

I wish that was true, though.


I've heard somewhere that there's a 50.5% chance of getting a boy because newborn boys die more commonly than newborn girls. Though I don't recall any sources to this.