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Ela 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{2}{*}{Coin} & heads & H-1 & H-2 & H-3 & H-4 & H-5 & H-6 \\
\hline
& tails & T-1 & T-2 & T-3 & T-4 & T-5 & T-6 \\
\hline
\end{tabular}

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



Answer :

GinnyAnswer
Sure! Let's proceed step by step.

First, let's complete the table:

\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] \\
\hline & 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 table now shows all possible outcomes when Ela rolls a die and then flips a coin. Each cell represents a unique outcome in the sample space.

Next, let's determine the size of the sample space.

Since there are 6 possible outcomes for the die (1 through 6) and 2 possible outcomes for the coin (heads and tails), the size of the sample space is
[tex]\[ 6 \text{ die outcomes} \times 2 \text{ coin outcomes} = 12 \text{ possible outcomes}. \][/tex]

So, the size of the sample space is [tex]\(\boxed{12}\)[/tex].

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