1. **Problem:** Two dice are rolled. Find the probability of getting: i. A sum of 6 or 11. ii. A sum greater than 10. 2. **Formula and Rules:** The total number of outcomes when two dice are rolled is $6 \times 6 = 36$. Probability of an event $E$ is given by: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Step i: Sum of 6 or 11** - Possible pairs for sum 6: $(1,5), (2,4), (3,3), (4,2), (5,1)$ → 5 outcomes. - Possible pairs for sum 11: $(5,6), (6,5)$ → 2 outcomes. - Total favorable outcomes = $5 + 2 = 7$. - Probability: $$P(6 \text{ or } 11) = \frac{7}{36}$$ 4. **Step ii: Sum greater than 10** - Possible sums greater than 10 are 11 and 12. - Sum 11 outcomes: 2 (as above). - Sum 12 outcomes: $(6,6)$ → 1 outcome. - Total favorable outcomes = $2 + 1 = 3$. - Probability: $$P(>10) = \frac{3}{36} = \frac{\cancel{3}}{\cancel{36}} = \frac{1}{12}$$ **Final answers:** - Probability of sum 6 or 11 is $\frac{7}{36}$. - Probability of sum greater than 10 is $\frac{1}{12}$.