1. **Stating the problem:** We roll a fair six-sided die and define event $E$ as getting an even number. 2. **Understanding the sample space:** The sample space $S$ for a six-sided die is $\{1, 2, 3, 4, 5, 6\}$. 3. **Defining event $E$:** Event $E$ consists of outcomes where the number rolled is even. So, $E = \{2, 4, 6\}$. 4. **Using the axiomatic approach of probability:** The probability of an event $E$ is given by $$P(E) = \frac{|E|}{|S|}$$ where $|E|$ is the number of favorable outcomes and $|S|$ is the total number of outcomes. 5. **Calculating the probability:** Here, $|E| = 3$ (since 2, 4, and 6 are even) and $|S| = 6$. 6. **Simplifying the fraction:** $$P(E) = \frac{3}{6} = \frac{\cancel{3}}{\cancel{6}} = \frac{1}{2}$$ 7. **Final answer:** The probability of rolling an even number is $\boxed{\frac{1}{2}}$.