Answer
$\frac{1}{4}.$, independent
Work Step by Step
Two events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the gender of the first child doesn't affect the second one, hence here sampling was done without replacement and $P(B|A)=P(B)$. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}.$
