To determine the sample space of outcomes for a fair, 9-sided number cube, we need to consider all the possible results that could occur when the cube is rolled.
A fair 9-sided number cube has sides numbered consecutively from 1 to 9. Therefore, each number on the cube is equally likely to occur when rolled.
Consequently, the sample space, which is the set of all possible outcomes, includes all numbers from 1 to 9. We list them as follows:
[tex]\[ S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \][/tex]
So, when rolling a fair 9-sided number cube, every roll will result in one of these numbers: 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Therefore, the correct sample space is:
[tex]\[ S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \][/tex]
