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

How about like this:

Your friend has two kids. One of them is named Nathan after his father. What are the odds the other one is a boy?

Scenario 1: The younger child is named Nathan (50%)
- 25% chance that the older child is a boy
- 25% chance that the older child is a girl
Scenario 2: The older child is named Nathan (50%)
- 25% chance that the younger child is a boy
- 25% chance that the younger child is a girl

50%.

With the original phrasing, it can be understood three ways.
1. The question is referring to a particular kid of the two, and states that it is a boy. Therefore, the one not mentioned can either be a boy or a girl => 50%.
(To elaborate, there are four possibilities. The 'one' mentioned in the problem is blue:
B/B
B/B
B/G
G/B
The odds that the other is a boy is 2/4 = 50%.)
2. The question states that exactly one kid of the two is a boy, meaning that the 'other' child must be a girl => 0%.
3. The question states that at least one kid is a boy. Likewise, it can also be understood that the woman has at least two kids in the first place => indeterminate.

This is fun.