Write out the sample space for the given experiment. Use the letter R to indicate red, G to indicate green, and B to indicate blue. A die shows 3 different colors on it. Give the sample space for the next 2 rolls.

To determine the sample space for the experiment of rolling a die that shows three different colors (Red, Green, and Blue) for the next two rolls, we can follow these steps: 1. **Identify the possible outcomes for a single roll**: The die can show either Red (R), Green (G), or Blue (B). Therefore, the outcomes for one roll are: - R - G - B 2. **Determine the outcomes for two rolls**: Since each roll is independent, we can combine the outcomes of the first roll with the outcomes of the second roll. 3. **List all combinations**: The sample space for two rolls can be represented as pairs of outcomes (first roll, second roll). The combinations are: - (R, R) - (R, G) - (R, B) - (G, R) - (G, G) - (G, B) - (B, R) - (B, G) - (B, B) 4. **Write the sample space**: The complete sample space \( S \) for the two rolls can be expressed as: \[ S = \{ (R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B) \} \] Thus, the sample space for the next two rolls of the die is: \[ \{ (R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B) \} \]