Probability that girl who answers the door is the eldest girl? You know that a family has 3 children. You walk up to and knock on the front door of their house. A girl answers the door. 
What is the probability that the she is the eldest girl among the children?
Assume that all 3 children are home and equally likely to answer the door.
(I appreciate that with questions like this, the wording can be so crucial. If the question is in any way ambiguous, I would be delighted to have an explanation of why that is the case!)

Condition on whether the girl who opened the door is the eldest child overall, the middle child, or the youngest child.  Each of these occur with probability $\frac{1}{3}$.  We are told this within the problem statement.
The probability she is the eldest girl given that she is the eldest child is clearly $1$.
The probability that she is the eldest girl given that she is the middle child is the same as the probability the eldest child is a boy which is $\frac{1}{2}$.
The probability that she is the eldest girl given that she is the youngest child is the same as the probability that the two eldest children are both boys which is $\frac{1}{4}$.
This makes the overall probability:
$$\frac{1}{3}\left(1+\frac{1}{2}+\frac{1}{4}\right) = \frac{7}{12}$$
