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?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this communityThis 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.
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 $\frac{1}{2}$.