1. **Stating the problem:** Consider a bag containing 5 pebbles: 2 red, 2 blue, and 1 green. We randomly select one pebble. Define the random variable $X$ as the color of the pebble chosen. 2. **Listing the sample space:** The sample space $S$ consists of all possible outcomes when selecting one pebble: $$S = \{\text{Red}, \text{Blue}, \text{Green}\}$$ 3. **Counting the number of variable $X$:** The random variable $X$ can take 3 values corresponding to the colors: Red, Blue, Green. 4. **Conclusion:** The variable $X$ is categorical with 3 possible outcomes. 5. **Frequency:** - Red pebbles: 2 - Blue pebbles: 2 - Green pebbles: 1 6. **Probability:** Total pebbles = 5 Probability of selecting each color: $$P(X=\text{Red}) = \frac{2}{5}$$ $$P(X=\text{Blue}) = \frac{2}{5}$$ $$P(X=\text{Green}) = \frac{1}{5}$$ 7. **Histogram:** The histogram would show bars for each color with heights proportional to their probabilities: Red and Blue bars at $\frac{2}{5}$, Green bar at $\frac{1}{5}$. Final answer: The random variable $X$ representing the color of a randomly selected pebble has probabilities $P(X=\text{Red})=\frac{2}{5}$, $P(X=\text{Blue})=\frac{2}{5}$, and $P(X=\text{Green})=\frac{1}{5}$.