A couple has 2 children. What is the probability that both are girls if the eldest is a girl? This is another question like this one. And by the same reason, the book only has the final answer, I'd like to check if my reasoning is right.
A couple has 2 children. What is the probability that both are girls if the eldest is a girl?

An alternative viewpoint:
For the eldest child to be a girl, they must have had a girl first. Therefore the probability of there being two girls is the probability of having a second girl which is $\frac{1}{2}$.
