1. In an experiment, Sienna places three marbles in a bag. One of the marbles is blue, one is red, and one is black. As part of the experiment, she pulls a marble out of the bag and replaces it ten times. Every time she pulls out a red marble, she records it. In this experiment, what makes up the sample space? pulling a marble out of the bag and having it be the red one pulling a marble out of the bag pulling a marble ten times pulling a red marble, a blue marble, or a black marble

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The sample space is the set of all possible outcomes you could get from doing the experiment. In this experiment, Sienna pulls a marble out of the bag 10 times (with replacement). On each pull, there are three possible outcomes: red, blue, or black. That means each single pull can result in one of the outcomes from {red, blue, black}.

Because the experiment involves 10 pulls, every outcome of the experiment is a sequence (or 10‑tuple) of colors. For example, one outcome might be

(red, blue, red, black, red, red, blue, black, blue, red).

So formally, the sample space is the set of all 10‑tuples where each entry is red, blue, or black—that is, {red, blue, black}^10.

Looking at the options given:

1. "pulling a marble out of the bag and having it be the red one"  
 – This option only describes one specific outcome on a single trial.

2. "pulling a marble out of the bag"  
 – This is the procedure rather than the outcomes.

3. "pulling a marble ten times"  
 – This states the number of pulls but doesn’t describe the outcomes of those pulls.

4. "pulling a red marble, a blue marble, or a black marble"  
 – This option correctly lists the possible outcomes of one pull. When considering that the experiment is repeated 10 times, the full sample space is the set of all sequences of these outcomes.

Thus, the best description of what makes up the sample space in this experiment is that each pull can result in a red, blue, or black marble—and over 10 pulls, the sample space is all sequences (of length 10) having these outcomes.
The sample space consists of all possible sequences of 10 marbles, where each marble can be red, blue, or black.

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