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A bucket contains three slips of paper. One of the following colors is written on each slip of paper: Red, Blue, and Yellow.

\begin{tabular}{|l|l|l|l|}
\hline List 1 & \multicolumn{1}{|c|}{ List 2 } & \multicolumn{1}{|c|}{ List 3 } & \multicolumn{1}{|c|}{ List 4 } \\
\hline Red & Red, Blue & Red, Red & Red, Red, Red \\
\hline Blue & Red, Yellow & Red, Blue & Red, Blue, Yellow \\
\hline Yellow & Blue, Red & Red, Yellow & Red, Yellow, Blue \\
\hline Red & Blue, Yellow & Blue, Blue & Blue, Blue, Blue \\
\hline Blue & Yellow, Red & Blue, Red & Blue, Red, Yellow \\
\hline Yellow & Yellow, Blue & Blue, Yellow & Blue, Yellow, Red \\
\hline Red & Red & Yellow, Yellow & Yellow, Yellow, Yellow \\
\hline Blue & Blue & Yellow, Red & Yellow, Red, Blue \\
\hline Yellow & Yellow & Yellow, Blue & Yellow, Blue, Red \\
\hline
\end{tabular}

Which list gives the sample space for pulling two slips of paper out of the bucket with replacement?

A. List 1
B. List 2
C. List 3
D. List 4



Answer :

GinnyAnswer
Sure, let's determine which list provides the sample space for pulling two slips of paper out of the bucket with replacement.

Given:
- There are three slips of paper, each labeled with one of three colors: Red, Blue, and Yellow.

When pulling two slips of paper out of the bucket with replacement, each drawing is independent and the total number of possible outcomes can be calculated.

Let's list out the possible outcomes:
1. Pulling a Red slip first and then a Red slip again (Red, Red).
2. Pulling a Red slip first and then a Blue slip (Red, Blue).
3. Pulling a Red slip first and then a Yellow slip (Red, Yellow).
4. Pulling a Blue slip first and then a Red slip (Blue, Red).
5. Pulling a Blue slip first and then a Blue slip again (Blue, Blue).
6. Pulling a Blue slip first and then a Yellow slip (Blue, Yellow).
7. Pulling a Yellow slip first and then a Red slip (Yellow, Red).
8. Pulling a Yellow slip first and then a Blue slip (Yellow, Blue).
9. Pulling a Yellow slip first and then a Yellow slip again (Yellow, Yellow).

Now, looking at the given lists:

- List 1 includes outcomes with a single draw, hence it's not appropriate.
- List 2 includes outcomes for pairs of draws, precisely what we need.
- List 3 includes repeated or combinations of multiple draws rather than pairs.
- List 4 includes triple draws, which is not what we are looking for.

So, the list that provides the sample space for pulling two slips of paper out of the bucket with replacement is List 2.

Thus, the correct answer is: List 2.

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