1. **Problem statement:** A die is rolled once. Find the probability that the outcome is: (a) not a 4 (b) exactly 6 (c) more than 3 2. **Formula and rules:** The probability of an event $E$ is given by $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ A fair six-sided die has outcomes $\{1,2,3,4,5,6\}$, so total outcomes = 6. 3. **Part (a): Probability not a 4** - Favorable outcomes: $\{1,2,3,5,6\}$ (all except 4) - Number of favorable outcomes = 5 - Probability: $$P(\text{not }4) = \frac{5}{6}$$ 4. **Part (b): Probability exactly 6** - Favorable outcome: $\{6\}$ - Number of favorable outcomes = 1 - Probability: $$P(6) = \frac{1}{6}$$ 5. **Part (c): Probability more than 3** - Outcomes more than 3: $\{4,5,6\}$ - Number of favorable outcomes = 3 - Probability: $$P(>3) = \frac{3}{6} = \frac{1}{2}$$ **Final answers:** - (a) $\frac{5}{6}$ - (b) $\frac{1}{6}$ - (c) $\frac{1}{2}$