To solve the problem and identify all the possible outcomes when Rhianna spins the spinner and tosses a coin, we'll consider each distinct scenario formed by a combination of coin tosses and spinner results.
1. Coin Toss Outcomes: There are two possible results when tossing a coin:
- Heads (H)
- Tails (T)
2. Spinner Outcomes: There are four possible results when spinning the spinner, as it's divided into four equal parts and numbered 1, 2, 3, and 4.
By combining every result from the coin toss with every result from the spinner, we can generate all possible outcomes. To find these combined results, we'll consider each combination:
- When the coin lands on Heads (H):
1. Heads and 1 (H1)
2. Heads and 2 (H2)
3. Heads and 3 (H3)
4. Heads and 4 (H4)
- When the coin lands on Tails (T):
5. Tails and 1 (T1)
6. Tails and 2 (T2)
7. Tails and 3 (T3)
8. Tails and 4 (T4)
Thus, the following are the possible outcomes from the combined experiment:
['H1', 'T1', 'H2', 'T2', 'H3', 'T3', 'H4', 'T4']
Now, let's match these outcomes to the presented tables.
The table showing all these outcomes would look like:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline H & H1 & H2 & H3 & H4 \\
\hline T & T1 & T2 & T3 & T4 \\
\hline
\end{array}
\][/tex]
This table accurately displays each possible outcome:
- Each column represents the outcome combining the coin result with a spinner number.
- Row 'H' contains outcomes when the coin lands on heads (H1, H2, H3, H4).
- Row 'T' contains outcomes when the coin lands on tails (T1, T2, T3, T4).
Thus, the correct table displaying all the possible outcomes is:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 \\
\hline T & T1 & T2 & T3 & T4 \\
\hline H & H1 & H2 & H3 & H4 \\
\hline
\end{array}
\][/tex]
