1. **Problem:** A four-sided die labelled 1, 2, 3, and 4 is rolled and a spinner labelled 3, 6, and 9 is spun. Create a table to show the sample space. 2. **Sample Space Table:** The sample space consists of all possible sums of the die roll and spinner result. 3. **Constructing the table:** Rows represent die outcomes (1 to 4), columns represent spinner outcomes (3, 6, 9). Each cell is the sum of row + column. $$\begin{array}{c|ccc} + & 3 & 6 & 9 \\ \hline 1 & 1+3=4 & 1+6=7 & 1+9=10 \\ 2 & 2+3=5 & 2+6=8 & 2+9=11 \\ 3 & 3+3=6 & 3+6=9 & 3+9=12 \\ 4 & 4+3=7 & 4+6=10 & 4+9=13 \end{array}$$ 4. **Answer:** The sample space table is: | | 3 | 6 | 9 | |---|---|---|---| | 1 | 4 | 7 | 10| | 2 | 5 | 8 | 11| | 3 | 6 | 9 | 12| | 4 | 7 |10 | 13| 5. **Problem:** What is $P(\text{sum even number})$? 6. **Step:** Count even sums in the table: - Even sums: 4, 6, 8, 10, 12 - Count occurrences: - 4 (1,3) - 6 (3,3) - 8 (2,6) - 10 (1,9), (4,6) - 12 (3,9) Total even sums = 6 7. **Total outcomes:** $4 \times 3 = 12$ 8. **Probability:** $$P(\text{sum even}) = \frac{6}{12} = \frac{1}{2}$$ **Final answer:** $\boxed{\frac{1}{2}}$