Use a tree diagram or table to determine the sample space for an experiment in which an eight-sided number cube is rolled twice. How many different possible outcomes are there?

Answer 1

To determine the sample space for rolling an eight-sided number cube twice, we can use a tree diagram.

Let's label the first roll as R1 and the second roll as R2. Each roll can result in numbers 1 through 8.

The tree diagram can show the possible outcomes for each roll:

```
R1 R2
1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
2 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
3 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
4 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
5 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
6 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
7 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
8 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
```

There are a total of 8 * 8 = 64 possible outcomes when rolling an eight-sided number cube twice.