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

The way you asked the question is too ambiguous.

There are two ways to interpret this.

1)
A women has a child. It's a boy.
A woman has another child. What gender is it?

Since those are two independent events, there is (non-biologically speaking), a 50% chance of having a male or female child

and

2)
The way you actually meant you question to be phrased.

I suggest next time you phrase it better so there is no ambiguity.