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?
(A) $\frac{2}{3}$
(B) $\frac{1}{4}$
(C) $\frac{1}{2}$
(D) $\frac{1}{3}$
(E) $\frac{1}{8}$
Since it is equally likely that a child is a boy as it is that a child is a girl, then the probability that any child is a girl is $\frac{1}{2}$.

The probability of any child being born a girl is independent of the number or gender of any children already born into the family.

That is, the probability of the second child being a girl is also $\frac{1}{2}$, as is the probability of the third child being a girl.

Therefore, the probability that all 3 children are girls is $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}=\frac{1}{8}$.

ANswer: (E)