Let's define the sample space for the event of picking two toys, one after the other (with replacement). We'll denote the toys as follows:
- G for giraffe
- P for panda
- M for monkey
- T for teddy bear
When Kelly picks a toy from the basket and then replaces it, each pick is independent. Therefore, each pick has 4 possible outcomes. Since she does this twice, the total sample space is [tex]\( 4 \times 4 = 16 \)[/tex] possible outcomes.
Let's organize these outcomes in a structured list based on the given question's format. The rows and columns indicate the outcomes of the first and the second pick, respectively:
1. First pick is a giraffe (G):
- Both picks giraffe: G-G
- First giraffe, second panda: G-P
- First giraffe, second monkey: G-M
- First giraffe, second teddy bear: G-T
2. First pick is a panda (P):
- First panda, second giraffe: P-G
- Both picks panda: P-P
- First panda, second monkey: P-M
- First panda, second teddy bear: P-T
3. First pick is a monkey (M):
- First monkey, second giraffe: M-G
- First monkey, second panda: M-P
- Both picks monkey: M-M
- First monkey, second teddy bear: M-T
4. First pick is a teddy bear (T):
- First teddy bear, second giraffe: T-G
- First teddy bear, second panda: T-P
- First teddy bear, second monkey: T-M
- Both picks teddy bear: T-T
Given our understanding, let's fill in the missing outcomes in the provided organized list:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{\text{Sample Space}} \\
\hline G-G & P-G & M-G & T-G \\
\hline G-P & \text{P-P} & M-P & T-P \\
\hline G-M & P-M & \text{M-M} & T-M \\
\hline G-T & P-T & M-T & \text{T-T} \\
\hline
\end{array}
\][/tex]
Thus, the missing outcomes are:
1. [tex]\( \text{P-P} \)[/tex] (Second row, second column)
2. [tex]\( \text{M-M} \)[/tex] (Third row, third column)
3. [tex]\( \text{T-T} \)[/tex] (Fourth row, fourth column)
The complete and organized sample space is:
```
[['G-G', 'P-G', 'M-G', 'T-G'], ['G-P', 'P-P', 'M-P', 'T-P'], ['G-M', 'P-M', 'M-M', 'T-M'], ['G-T', 'P-T', 'M-T', 'T-T']]
```
