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

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.