Let’s complete the table of scores by considering all possible outcomes when Avner multiplies the values from Spinner A and Spinner B.
Spinner A can land on the numbers 1, 2, or 3.
Spinner B can land on the numbers 1, 2, 3, or 4.
To find the score, we multiply the number from Spinner A by the number from Spinner B. We will fill in each cell of the table by calculating these products.
1. For Spinner B landing on 2:
- If Spinner A lands on 1, the score is [tex]\(2 \times 1 = 2\)[/tex].
- If Spinner A lands on 2, the score is [tex]\(2 \times 2 = 4\)[/tex].
- If Spinner A lands on 3, the score is [tex]\(2 \times 3 = 6\)[/tex].
2. For Spinner B landing on 3:
- If Spinner A lands on 1, the score is [tex]\(3 \times 1 = 3\)[/tex].
- If Spinner A lands on 2, the score is [tex]\(3 \times 2 = 6\)[/tex].
- If Spinner A lands on 3, the score is [tex]\(3 \times 3 = 9\)[/tex].
3. For Spinner B landing on 4:
- If Spinner A lands on 1, the score is [tex]\(4 \times 1 = 4\)[/tex].
- If Spinner A lands on 2, the score is [tex]\(4 \times 2 = 8\)[/tex].
- If Spinner A lands on 3, the score is [tex]\(4 \times 3 = 12\)[/tex].
Combining these calculations, we complete the table as follows:
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\cline { 2 - 4 } \multicolumn{2}{|c|}{} & \multicolumn{3}{|c|}{Spinner A} \\
\cline { 2 - 4 } & 1 & 2 & 3 \\
\hline \multirow{3}{*}{Spinner B} & 1 & 1 & 2 & 3 \\
\cline { 2 - 5 } & 2 & 2 & 4 & 6 \\
\cline { 2 - 5 } & 3 & 3 & 6 & 9 \\
\cline { 2 - 5 } & 4 & 4 & 8 & 12 \\
\hline
\end{tabular}
\][/tex]
