1. **Problem Statement:** Austin rolls a red die and a black die, both six-sided. The red die shows 4. Austin wins a point if the sum of the two dice is greater than 8. 2. **Part a) Are the two events dependent or independent?** - The two events are: (i) red die shows 4, (ii) sum of dice is greater than 8. - Since the red die result is fixed at 4, the sum depends entirely on the black die. - The outcome of the black die affects the sum, so the events are dependent. 3. **Part b) Probability Austin wins a point:** - Given red die = 4, sum $= 4 + \text{black die}$. - Austin wins if $4 + \text{black die} > 8$. - Simplify inequality: $\text{black die} > 4$. - Possible black die outcomes: 1, 2, 3, 4, 5, 6. - Outcomes satisfying $\text{black die} > 4$ are 5 and 6. - Number of favorable outcomes = 2. - Total possible outcomes for black die = 6. - Probability $= \frac{2}{6} = \frac{1}{3}$. 4. **Summary:** - Events are dependent because the sum depends on the black die given the red die is fixed. - Probability Austin wins a point is $\frac{1}{3}$.