Let's fill in the missing cells in the table and determine the size of the sample space.
First, the missing cells can be identified as follows:
1. In the row for heads (Coin) and the column for die roll 4:
- The cell should be "H-4"
2. In the row for tails (Coin) and the column for die roll 2:
- The cell should be "T-2"
3. In the row for tails (Coin) and the column for die roll 6:
- The cell should be "T-6"
Updating the table with this information:
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& & \multicolumn{6}{|c|}{ Die } \\
\hline
& & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
\multirow{2}{*}{ Coin } & heads & [tex]$H -1$[/tex] & [tex]$H -2$[/tex] & [tex]$H -3$[/tex] & [tex]$H-4$[/tex] & H-5 & [tex]$H -6$[/tex] \\
\hline
& tails & [tex]$T -1$[/tex] & [tex]$T-2$[/tex] & [tex]$T -3$[/tex] & T-4 & T-5 & [tex]$T-6$[/tex] \\
\hline
\end{tabular}
Next, we calculate the size of the sample space. For each result on the coin (heads (H) or tails (T)), there are 6 possible outcomes of the die (1 through 6). Therefore, the sample space size is:
2 outcomes (coin) [tex]\( \times \)[/tex] 6 outcomes (die) = 12
So, the size of the sample space is 12.
Therefore, the table is updated and completed as shown above, and the sentence provided would be filled as:
The size of the sample space is [tex]\(12\)[/tex].
