A bag has six balls labeled \( A, B, C, D, E \), and \( F \). One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter \( A \) or \( C \). If there is more than one element in the set, separate them with commas. Sample space: \( \{1\} \) Event of choosing the letter \( A \) or \( C:\{\square\} \)

To solve this problem, we will first identify the sample space and then the specific event of choosing the letter \( A \) or \( C \). 1. **Sample Space**: The sample space is the set of all possible outcomes when one ball is randomly picked from the bag. Since the balls are labeled \( A, B, C, D, E, \) and \( F \), the sample space can be represented as: \[ S = \{ A, B, C, D, E, F \} \] 2. **Event of Choosing the Letter \( A \) or \( C \)**: The event of choosing either \( A \) or \( C \) consists of the outcomes that include these letters. Therefore, the event can be represented as: \[ E = \{ A, C \} \] Now, we can summarize the results: - Sample space: \( \{ A, B, C, D, E, F \} \) - Event of choosing the letter \( A \) or \( C: \{ A, C \} \)