1. **State the problem:** We want to find the probability $P[A]$ of rolling a total of 2, 3, 4, or 5 with two dice. 2. **Sample space:** The total number of possible outcomes when rolling two dice is 36. 3. **Event A outcomes:** The pairs that sum to 2, 3, 4, or 5 are: $$\{(1,1), (1,2), (2,1), (1,3), (2,2), (3,1), (1,4), (2,3), (3,2), (4,1)\}$$ There are 10 such outcomes. 4. **Probability formula:** $$P[A] = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 5. **Calculate probability:** $$P[A] = \frac{10}{36}$$ 6. **Simplify fraction:** $$P[A] = \frac{\cancel{10}}{\cancel{36}} = \frac{5}{18}$$ 7. **Final answer:** $$P[A] = \frac{5}{18}$$ This means the probability of rolling a total of 2, 3, 4, or 5 with two dice is $\frac{5}{18}$.