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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 (H is heads and T 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{3}{*}{ 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
Let's fill in the missing entries in the table and determine the size of the sample space based on the given outcomes:

First, we complete the table for the compound event where Ella rolls a die and then flips a coin.

The table is as follows:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & & \multicolumn{6}{|c|}{ Die } \\ \hline & & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{3}{*}{ Coin } & Heads & H-1 & H-2 & H-3 & H-4 & H-5 & H-6 \\ \cline { 2 - 8 } & Tails & T-1 & T-2 & T-3 & T-4 & T-5 & T-6 \\ \hline \end{tabular} \][/tex]

We filled the missing values (H-4 for heads and T-2, T-6 for tails).

Now, we complete the sentence beneath the table regarding the size of the sample space:

The size of the sample space is 12.

Let's rewrite the filled version:

1. Table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & & \multicolumn{6}{|c|}{ Die } \\ \hline & & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{3}{*}{ Coin } & Heads & H-1 & H-2 & H-3 & H-4 & H-5 & H-6 \\ \cline { 2 - 8 } & Tails & T-1 & T-2 & T-3 & T-4 & T-5 & T-6 \\ \hline \end{tabular} \][/tex]
2. Sentence completion:
The size of the sample space is 12.

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