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

However, the "B / B" option has already been covered in the scenario when looking at the first child being male, e.g. B / B.

Discounting this gives 3 possible outcomes
B / G
B / B
G / B

All of which are equally likely to happen. Therefore, its 1/3 chance or 33%.

So it doesn't matter if you're older than your older brother eh?
B/B is not the same as B/B

So it doesn't matter if you're older than your older brother eh?
B/B is not the same as B/B

Its not the same if we are not taking order into account. The question simply says if one of the children are male. It doesn't specify which child is male.
If the we know the order, then the answer will be 50%.
But as we don't know the order we have to look at all the possibilities than can occur with either child being the male in question.

Its a common error to make. A similar example that highlights these two different scenarios would be:
Scenario 1:
Two people need to be picked to fill the position of Chairperson and Secretary.
If the Chairperson is male, what is the probability of the Secretary also being male
In this scenario B / B is different to B / B as the first B would be the Chairperson, the second being the Secretary

Scenario 2:
Two people need to be picked to represent a committee at a meeting.
If one of the people picked is male, what is the probability of the other person also being male.
In this scenario B / B is the same as B / B as both people will be going to the meeting and neither will be filling a separate position.

Scenario 2 is the same question as put forward by the Opeth.
Scenario 1 is the same misunderstanding being made by those arguing for 50%

It's 50%. You asked "what are the odds the other is a boy" not "what are the odds of having 2 boys in a row" (this 2nd option would in fact be 33% like you said).

So it's 50% chance of having a boy

It's 50%. You asked "what are the odds the other is a boy" not "what are the odds of having 2 boys in a row" (this 2nd option would in fact be 33% like you said).

So it's 50% chance of having a boy

This.

How'd this get revived -_-

Yes, but assuming 50% of each, these are wrong.

They're not going to name both kids Nathan (well, let's hope) - so the options are these:
Girl/Girl (eliminated)
Boy/Girl (Older child named Nathan)
Girl/Boy (Younger child named Nathan)
Boy/Boy (One child named Nathan)
These 4 scenarios happen with equal likelihood, so the remaining ones all have 1 in 3 chance of happening now that one is gone (due to knowledge that at least one is a boy)

If we assume it's a 50% chance the older or younger child is named Nathan, that means:
- 1/3 + 1/6 the older child is Nathan = 50%
- 1/3 + 1/6 the younger child is Nathan = 50%

That's 1/3 (other child is a girl) + 1/6 (other child is a boy)
Total: 2/3 of the time, the other kid is a girl.


@ClawofBeta, the problem is not that the events are independent, it's that the information given is ambiguous about which event happened.

...yeah, you're right. My bad.

The original wording was unclear, though.