Difference between “at least one out of two children is a girl” and “a random child out of two is a girl”

Question

I'm struggling with the intuition here. I'm reading the Probability book by Blitzstein, where three situations are contrasted:

1. There are two children, the eldest is a girl, what is the probability the youngest is also a girl? (1/2)
2. There are two children, at least one is a girl, what is the probability the other is also a girl? (1/3)
3. There are two children, you run into a random one on the street, and it's a girl, what is the probability the other is also a girl? (1/2)

Now, I understand the difference between situation 1 and situation 2: situation 1 has sample space {GG, GB, BG, BB}, and by knowing the eldest is a girl, this reduces the conditional universe to {GG, GB}. Situation 2 has the same sample space, but the conditional universe only reduces to {GG, GB, BG}. This all makes sense. However, I don't understand the difference between situation 2 and situation 3. Intuitively, my reasoning is that in both cases at least one child is a girl, and no information is given about whether it's the eldest or the youngest child, so they should have the same probability. Where is my reasoning mistaken?

Answer 1

I'm assuming that since it says "also a girl" in 3, it means you saw the child in the street is a girl. Given that, the other child could be boy or girl. It's the same as in situation 1, you know the exact status of a specific child, and it has no influence on the other child