Questions: A bag has five balls labeled A, B, C, D, and E. 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 a letter from A to C. If there is more than one element in the set, separate them with commas. Sample space: Event of choosing a letter from A to C:

Solution Steps

To solve this problem, we need to identify all possible outcomes when picking a ball from the bag, which forms the sample space. Then, we need to identify the subset of outcomes that correspond to picking a letter from $A$ to $C$.

1. List all possible outcomes (sample space) when picking a ball from the bag.
2. Identify the subset of outcomes that correspond to picking a letter from $A$ to $C$.

The sample space \( S \) describes all possible outcomes when one ball is randomly picked from the bag. The balls are labeled \( A, B, C, D, \) and \( E \). Therefore, the sample space is given by: \[ S = \{ A, B, C, D, E \} \]

The event \( E \) of choosing a letter from \( A \) to \( C \) includes the outcomes that fall within this range. Thus, the event is represented as: \[ E = \{ A, B, C \} \]

Final Answer