Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling the number 1,3 , or 4 . If there is more than one element in the set, separate them with commas. Sample space: \( \{\square\} \) Event of rolling the number 1,3, or \( 4:\{\square\} \)

To solve this problem, we need to define the sample space for rolling a standard six-sided die and then identify the specific outcomes for the event of rolling the numbers 1, 3, or 4. 1. **Sample Space**: The sample space \( S \) for rolling a six-sided die includes all possible outcomes, which are the numbers 1 through 6. Therefore, we can express the sample space as: \[ S = \{1, 2, 3, 4, 5, 6\} \] 2. **Event of Rolling the Numbers 1, 3, or 4**: The event \( E \) that we are interested in consists of the outcomes where the die shows either 1, 3, or 4. Thus, we can express this event as: \[ E = \{1, 3, 4\} \] Now, we can summarize the results: - Sample space: \( S = \{1, 2, 3, 4, 5, 6\} \) - Event of rolling the number 1, 3, or 4: \( E = \{1, 3, 4\} \)