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Ella rolls a die and then flips a coin. The sample space for this compound event is represented in the table ([tex]$H$[/tex] is heads and [tex]$T$[/tex] is tails). Complete the table and the sentence beneath it.

\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] & [tex]$H-5$[/tex] & [tex]$H-6$[/tex] \\
\cline{2-8}
& tails & [tex]$T-1$[/tex] & [tex]$T-2$[/tex] & [tex]$T-3$[/tex] & [tex]$T-4$[/tex] & [tex]$T-5$[/tex] & [tex]$T-6$[/tex] \\
\hline
\end{tabular}

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



Answer :

GinnyAnswer
To complete the table, follow these steps:

1. Notice that missing elements are present in the "heads" and "tails" rows for the die rolls.
2. Identify the missing values by considering sequential numbering and corresponding to the roll of the die:

For the "heads" row:
- The only missing entry is for die roll 4, which should be "H-4".

For the "tails" row:
- The missing entry for die roll 2 should be "T-2".
- The missing entry for die roll 6 should be "T-6".

Then, the table should be completed as:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline & & \multicolumn{5}{|c|}{Die} \\ \hline & & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{3}{*}{Coin} & heads & $H-1$ & $H-2$ & $H-3$ & $H-4$ & $H-5$ & $H-6$ \\ \cline{2-8} & tails & $T-1$ & $T-2$ & $T-3$ & $T-4$ & $T-5$ & $T-6$ \\ \hline \end{tabular} \][/tex]

Next, consider the size of the sample space:
- There are 2 possible outcomes for the coin (heads and tails).
- There are 6 possible outcomes for the roll of a die (1 through 6).

Therefore, the size of the sample space is calculated by multiplying the number of outcomes for each event:
[tex]\[ 2 \times 6 = 12 \][/tex]

So, the complete sentence beneath the table should read:
"The size of the sample space is [tex]\(12\)[/tex]."

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