1. **State the problem:** We want to find the probability of having 7 girls in a family with 7 children, assuming each child is equally likely to be a girl or a boy. 2. **Formula used:** The probability of having exactly $k$ girls in $n$ births, with each birth independent and probability of girl $p=\frac{1}{2}$, is given by the binomial formula: $$P(k) = \binom{n}{k} p^k (1-p)^{n-k}$$ 3. **Apply the formula:** Here, $n=7$, $k=7$, and $p=\frac{1}{2}$. So, $$P(7) = \binom{7}{7} \left(\frac{1}{2}\right)^7 \left(1-\frac{1}{2}\right)^0 = 1 \times \left(\frac{1}{2}\right)^7 \times 1 = \left(\frac{1}{2}\right)^7$$ 4. **Calculate the power:** $$\left(\frac{1}{2}\right)^7 = \frac{1^7}{2^7} = \frac{1}{128}$$ 5. **Final answer:** The probability of having 7 girls is $$\boxed{\frac{1}{128}}$$ This fraction is already in simplest form.