Type the correct answer in each box.

There are three letter tiles (A, B, and C) in a bag, and there are three number tiles (1, 2, and 3) in another bag. Alexis picks a letter tile, and then she picks a number tile. Complete the table representing the sample space for this situation.

\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 & [tex]$\square$[/tex] & C-2 \\
\cline {2-5} & 3 & A-3 & B-3 & [tex]$\square$[/tex] \\
\hline
\end{tabular}

The sample size of the event is [tex]$\square$[/tex].



Answer :

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].