A standard cubical die has opposite faces summing to 7 (i.e., $1 \leftrightarrow 6$, $2 \leftrightarrow 5$, $3 \leftrightarrow 4$). The die is rolled twice: face 4 lands facing upwards on the first roll, and face 2 lands facing upwards on the second roll. The sum of the numbers on the bottom faces resting on the table for both rolls combined is:
Options:
(A) 6
(B) 7
(C) 8
(D) 9
Answer Key:
C
Step-by-Step Solution & Explanation
1. In any standard die, $\text{Top face} + \text{Bottom face} = 7$.
2. On Roll 1: Top $= 4 \implies \text{Bottom} = 7 - 4 = 3$.
3. On Roll 2: Top $= 2 \implies \text{Bottom} = 7 - 2 = 5$.
4. Combined sum of bottom faces $= 3 + 5 = 8$.