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. \( \begin{array}{l}\text { Answer } \\ \text { How to enter your answer (opens in new window) } \\ \text { Separate your answers using commas. }\end{array} \)

To determine the sample space for the experiment of rolling a die that shows three different colors (red \( R \), green \( G \), and blue \( B \)) for the next two rolls, we need to consider all possible outcomes for each roll. 1. **First Roll:** The die can show either \( R \), \( G \), or \( B \). 2. **Second Roll:** Similarly, the die can again show either \( R \), \( G \), or \( B \). Since each roll is independent, we can combine the outcomes of the first roll with the outcomes of the second roll. The possible outcomes for two rolls can be represented as ordered pairs, where the first element is the result of the first roll and the second element is the result of the second roll. The sample space \( S \) can be listed as follows: - \( (R, R) \) - \( (R, G) \) - \( (R, B) \) - \( (G, R) \) - \( (G, G) \) - \( (G, B) \) - \( (B, R) \) - \( (B, G) \) - \( (B, B) \) Thus, the sample space for the next two rolls is: \[ S = \{ (R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B) \} \] You can enter your answer as: \( (R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B) \)