Let's complete the table and find the sample size.
Given:
- There are three letter tiles: A, B, and C.
- There are three number tiles: 1, 2, and 3.
- Alexis picks a letter tile, then a number tile.
The table is partially filled, and we need to fill in the missing entries.
Initially, the table is:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Letter Tile } \\
\hline & & A & B & C \\
\hline & 1 & A-1 & B-1 & C-1 \\
\cline { 2 - 5 } Number Tile & 2 & A-2 & $\square$ & C-2 \\
\cline { 2 - 5 } & 3 & A-3 & B-3 & $\square$ \\
\hline
\end{tabular}
\][/tex]
From the given information, we know that the missing entries are [tex]\( B-2 \)[/tex] and [tex]\( C-3 \)[/tex].
So, the completed table will be:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Letter Tile } \\
\hline & & A & B & C \\
\hline & 1 & A-1 & B-1 & C-1 \\
\cline { 2 - 5 } Number Tile & 2 & A-2 & B-2 & C-2 \\
\cline { 2 - 5 } & 3 & A-3 & B-3 & C-3 \\
\hline
\end{tabular}
\][/tex]
Each row and each column in the table represent a possible outcome when picking a letter and a number.
To calculate the sample size of the event:
- There are 3 possible letter choices.
- There are 3 possible number choices.
Therefore, the sample size is:
[tex]\[ 3 \text{ letters} \times 3 \text{ numbers} = 9 \][/tex]
So, the sample size of the event is 9.
Putting it all together:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Letter Tile } \\
\hline & & A & B & C \\
\hline & 1 & A-1 & B-1 & C-1 \\
\cline { 2 - 5 } Number Tile & 2 & A-2 & B-2 & C-2 \\
\cline { 2 - 5 } & 3 & A-3 & B-3 & C-3 \\
\hline
\end{tabular}
\][/tex]
The sample size of the event is [tex]\( 9 \)[/tex].
