1. **State the problem:** We want to find the probability of having 2 girls in a family with 2 children, assuming each child is equally likely to be a girl or a boy. 2. **Formula and rules:** The probability of independent events both happening is the product of their individual probabilities. 3. **Calculate individual probabilities:** Probability of a girl in one birth is $\frac{1}{2}$. 4. **Calculate combined probability:** For 2 children, both girls, the probability is $$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.$$ 5. **Simplify the fraction:** $\frac{1}{4}$ is already in simplest form. **Final answer:** The probability of having 2 girls is $\frac{1}{4}$.