1. **State the problem:** We have two fair spinners. The left spinner has numbers 6, 3, 5, and 4. The right spinner has numbers 3, 4, and 4. We spin both and add their results. We need to find the sample space of all possible totals and the probability of scoring a total of 10. 2. **Sample space diagram:** The left spinner outcomes are $\{6,3,5,4\}$ and the right spinner outcomes are $\{3,4,4\}$. We list all possible sums: - $6 + 3 = 9$ - $6 + 4 = 10$ - $6 + 4 = 10$ - $3 + 3 = 6$ - $3 + 4 = 7$ - $3 + 4 = 7$ - $5 + 3 = 8$ - $5 + 4 = 9$ - $5 + 4 = 9$ - $4 + 3 = 7$ - $4 + 4 = 8$ - $4 + 4 = 8$ 3. **Count total outcomes:** The left spinner has 4 sections, the right spinner has 3 sections, so total outcomes = $4 \times 3 = 12$. 4. **Count outcomes with total 10:** From above, total 10 occurs twice: $(6+4)$ and $(6+4)$. 5. **Calculate probability:** $$ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{12} $$ 6. **Simplify fraction:** $$ \frac{2}{12} = \frac{\cancel{2}}{\cancel{12}} = \frac{1}{6} $$ **Final answer:** The probability of scoring a total of 10 is $\frac{1}{6}$.