2013 Gauss 8 Problem 16

A family has 3 children. It is equally likely that a child is a boy as it is that a child is a girl. What is the probability that the 3 children are all girls?

\textbf{(A)}\ \frac{2}{3}\quad \textbf{(B)}\ \frac{1}{4}\quad \textbf{(C)}\ \frac{1}{2}\quad \textbf{(D)}\ \frac{1}{3}\quad \textbf{(E)}\ \frac{1}{8}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.