To determine which table shows all the possible outcomes when spinning each spinner once, let's list all the possible outcomes for each combination of spinners:
- The first spinner has the values: [tex]\(2 A\)[/tex], [tex]\(4 A\)[/tex], [tex]\(6 A\)[/tex], [tex]\(8 A\)[/tex]
- The second spinner has the values: [tex]\(2 B\)[/tex], [tex]\(4 B\)[/tex], [tex]\(6 B\)[/tex], [tex]\(8 B\)[/tex]
We need to find all combinations of outcomes when both spinners are spun. The possible outcomes are:
1. [tex]\( (2 A, 2 B) \)[/tex]
2. [tex]\( (2 A, 4 B) \)[/tex]
3. [tex]\( (2 A, 6 B) \)[/tex]
4. [tex]\( (2 A, 8 B) \)[/tex]
5. [tex]\( (4 A, 2 B) \)[/tex]
6. [tex]\( (4 A, 4 B) \)[/tex]
7. [tex]\( (4 A, 6 B) \)[/tex]
8. [tex]\( (4 A, 8 B) \)[/tex]
9. [tex]\( (6 A, 2 B) \)[/tex]
10. [tex]\( (6 A, 4 B) \)[/tex]
11. [tex]\( (6 A, 6 B) \)[/tex]
12. [tex]\( (6 A, 8 B) \)[/tex]
13. [tex]\( (8 A, 2 B) \)[/tex]
14. [tex]\( (8 A, 4 B) \)[/tex]
15. [tex]\( (8 A, 6 B) \)[/tex]
16. [tex]\( (8 A, 8 B) \)[/tex]
Having identified all the possible outcomes, we need to match them to the correct table:
\begin{tabular}{|l|c|c|c|c|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & \multicolumn{4}{c|}{ First Spinner } \\
\hline
Second & [tex]$2 A$[/tex] & [tex]$4 A$[/tex] & [tex]$6 A$[/tex] & [tex]$8 A$[/tex] \\
\hline
Spinner & [tex]$2 B$[/tex] & [tex]$4 B$[/tex] & [tex]$6 B$[/tex] & [tex]$8 B$[/tex] \\
\hline
\end{tabular}
This is the correct table as it clearly details all the possible outcomes where each combination of the first spinner value with the second spinner value is represented appropriately.
