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Sagot :
To determine the table that shows all possible outcomes when Rhianna spins the spinner and tosses a coin, we need to consider the combinations of the outcomes from both the spinner and the coin toss.
The spinner is divided into four equal parts numbered 1, 2, 3, and 4. The coin has two outcomes: Heads (H) and Tails (T).
For each number on the spinner (1, 2, 3, 4), the coin can either land on Heads (H) or Tails (T). Therefore, the total number of possible outcomes is 4 (spinner) * 2 (coin) = 8 possible outcomes.
These outcomes can be listed as pairs (Coin, Spinner):
1. (H, 1)
2. (H, 2)
3. (H, 3)
4. (H, 4)
5. (T, 1)
6. (T, 2)
7. (T, 3)
8. (T, 4)
Now, let's match these outcomes to the given tables:
1.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline [tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline
\end{tabular}
In this table, all outcomes for Heads are correctly represented, but it repeats the row for Heads instead of showing the outcomes for Tails.
2.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline [tex]$T$[/tex] & [tex]$T 1$[/tex] & [tex]$T 2$[/tex] & [tex]$T 3$[/tex] & [tex]$T 4$[/tex] \\
\hline [tex]$T$[/tex] & [tex]$T 1$[/tex] & [tex]$T 2$[/tex] & [tex]$T 3$[/tex] & [tex]$T 4$[/tex] \\
\hline
\end{tabular}
This table has all outcomes for Tails but repeats the row for Tails instead of showing the outcomes for Heads.
3.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$H$[/tex] & H1 & T2 & H3 & T4 \\
\hline T & H1 & T2 & H3 & T4 \\
\hline
\end{tabular}
This table doesn’t accurately represent the combinations of the outcomes.
4.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$T$[/tex] & T1 & T2 & T3 & T4 \\
\hline[tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline
\end{tabular}
This table correctly displays all possible outcomes:
- The first row lists the outcomes when the coin lands on Heads (H): H1, H2, H3, H4.
- The second row lists the outcomes when the coin lands on Tails (T): T1, T2, T3, T4.
Thus, the fourth table is the correct one that shows all possible outcomes of Rhianna's spinner and coin toss.
The spinner is divided into four equal parts numbered 1, 2, 3, and 4. The coin has two outcomes: Heads (H) and Tails (T).
For each number on the spinner (1, 2, 3, 4), the coin can either land on Heads (H) or Tails (T). Therefore, the total number of possible outcomes is 4 (spinner) * 2 (coin) = 8 possible outcomes.
These outcomes can be listed as pairs (Coin, Spinner):
1. (H, 1)
2. (H, 2)
3. (H, 3)
4. (H, 4)
5. (T, 1)
6. (T, 2)
7. (T, 3)
8. (T, 4)
Now, let's match these outcomes to the given tables:
1.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline [tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline
\end{tabular}
In this table, all outcomes for Heads are correctly represented, but it repeats the row for Heads instead of showing the outcomes for Tails.
2.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline [tex]$T$[/tex] & [tex]$T 1$[/tex] & [tex]$T 2$[/tex] & [tex]$T 3$[/tex] & [tex]$T 4$[/tex] \\
\hline [tex]$T$[/tex] & [tex]$T 1$[/tex] & [tex]$T 2$[/tex] & [tex]$T 3$[/tex] & [tex]$T 4$[/tex] \\
\hline
\end{tabular}
This table has all outcomes for Tails but repeats the row for Tails instead of showing the outcomes for Heads.
3.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$H$[/tex] & H1 & T2 & H3 & T4 \\
\hline T & H1 & T2 & H3 & T4 \\
\hline
\end{tabular}
This table doesn’t accurately represent the combinations of the outcomes.
4.
\begin{tabular}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline[tex]$T$[/tex] & T1 & T2 & T3 & T4 \\
\hline[tex]$H$[/tex] & [tex]$H 1$[/tex] & [tex]$H 2$[/tex] & [tex]$H 3$[/tex] & [tex]$H 4$[/tex] \\
\hline
\end{tabular}
This table correctly displays all possible outcomes:
- The first row lists the outcomes when the coin lands on Heads (H): H1, H2, H3, H4.
- The second row lists the outcomes when the coin lands on Tails (T): T1, T2, T3, T4.
Thus, the fourth table is the correct one that shows all possible outcomes of Rhianna's spinner and coin toss.
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