1. **State the problem:** We have a box with 3 red balls and 5 blue balls. We draw 3 balls one by one with replacement, and we want to define the sample space for the colors recorded. 2. **Understanding the experiment:** Since the balls are drawn with replacement, after each draw the box still contains 3 red and 5 blue balls. Each draw is independent. 3. **Sample space definition:** The sample space consists of all possible ordered triples of colors drawn. Each position in the triple can be either Red (R) or Blue (B). 4. **Number of outcomes:** Since each draw has 2 possible outcomes (R or B), and there are 3 draws, the total number of outcomes is $$2^3 = 8$$. 5. **List the sample space:** $$\{ (R,R,R), (R,R,B), (R,B,R), (R,B,B), (B,R,R), (B,R,B), (B,B,R), (B,B,B) \}$$ This set represents all possible sequences of colors drawn in order with replacement.