1. **Problem statement:** A card numbered from 1 to 9 is selected randomly, and a fair six-sided die is rolled once. We want to find the probability that the sum of the two numbers is a perfect square. 2. **Possible sums:** The card can be any number from 1 to 9, and the die can be any number from 1 to 6. So the sums range from $1+1=2$ to $9+6=15$. 3. **Perfect squares in this range:** The perfect squares between 2 and 15 are $4, 9,$ and $16$. Since 16 is not possible (max sum is 15), we consider $4$ and $9$. 4. **Calculate pairs for sum = 4:** - Possible pairs $(card, die)$ such that $card + die = 4$ are: - $(1,3), (2,2), (3,1)$ - Number of pairs: 3 5. **Calculate pairs for sum = 9:** - Possible pairs $(card, die)$ such that $card + die = 9$ are: - $(3,6), (4,5), (5,4), (6,3), (7,2), (8,1)$ - Number of pairs: 6 6. **Total favorable pairs:** $3 + 6 = 9$ 7. **Total possible pairs:** Since the card has 9 options and the die has 6 options, total pairs = $9 \times 6 = 54$ 8. **Probability:** $$\text{Probability} = \frac{\text{favorable pairs}}{\text{total pairs}} = \frac{9}{54} = \frac{1}{6}$$ **Final answer:** $\boxed{\frac{1}{6}}$ which corresponds to option B.