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?

The sample space is $S = \{(g,g),(g,b),(b,g),(b,b)\}$, where $b$ is for boy, $g$ is for girl the first element of the tuple is the eldest.
Let $B$ the event the eldest is a girl, so $B=\{(g,b),(g,g)\}$. 
$A$ is the event where the two children are girls. $A = \{(g,g)\}$.
Then:
$$ P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\dfrac{|A\cap B|}{|S|}}{\dfrac{|B|}{|S|}}=\frac{1}{2}$$.
The end.
