1. **Stating the problem:** A die is thrown once. We want to find the probability of three events: (a) The score is greater than 3. (b) The score is less than 3. (c) The score is less than 3 or greater than 3. 2. **Formula and rules:** The probability of an event $E$ is given by: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ For a fair six-sided die, total outcomes = 6 (faces 1 to 6). 3. **Calculations:** (a) Score > 3 means the outcomes are 4, 5, 6. Number of favorable outcomes = 3. $$P(>3) = \frac{3}{6} = \frac{\cancel{3}}{\cancel{6}} = \frac{1}{2}$$ (b) Score < 3 means the outcomes are 1, 2. Number of favorable outcomes = 2. $$P(<3) = \frac{2}{6} = \frac{\cancel{2}}{\cancel{6}} = \frac{1}{3}$$ (c) Score less than 3 or greater than 3 means outcomes are 1, 2, 4, 5, 6. Number of favorable outcomes = 5. $$P(<3 \text{ or } >3) = \frac{5}{6}$$ 4. **Summary:** - Probability(score > 3) = $\frac{1}{2}$ - Probability(score < 3) = $\frac{1}{3}$ - Probability(score < 3 or > 3) = $\frac{5}{6}$