To determine the sample space for rolling an eight-sided number cube (which has numbers from 1 to 8) twice, we can either use a tree diagram or a table to organize the possible outcomes.
Tree Diagram
- First Roll: There are 8 possible outcomes: 1, 2, 3, 4, 5, 6, 7, 8.
- Second Roll: For each outcome of the first roll, there are again 8 possible outcomes.
The tree diagram would show each outcome of the first roll branching out to all possible outcomes of the second roll:
- For example:
- From
1, the outcomes of the second roll could be:1, 2, 3, 4, 5, 6, 7, 8(resulting in: 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8) - From
2:2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8 - ...
- From
8:8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8
- From
Sample Space Calculation
In total, for each of the 8 outcomes in the first roll, there are 8 outcomes in the second roll:
\[ \text{Total outcomes} = 8 \text{ (first roll)} \times 8 \text{ (second roll)} = 64 \text{ outcomes} \]
Conclusion
Thus, the sample space includes 64 different possible outcomes when an eight-sided number cube is rolled twice.
So, the answer is 64 outcomes.