Let's analyze and answer the question in the image step by step.

Problem Breakdown:

1. Sample Space: The bag contains six balls labeled $A, B, C, D, E, F$. The sample space is the set of all possible outcomes when one ball is randomly picked.

   Sample Space = $\{A, B, C, D, E, F\}$

2. Event of choosing the letter $C$: This event consists of the outcome where the letter $C$ is chosen.

   Event of choosing $C$ = $\{C\}$

Final Answer:

• Sample space: $\{A, B, C, D, E, F\}$
• Event of choosing the letter $C$: $\{C\}$

Would you like further details or have any questions?

Related Questions:

1. What is the probability of picking $C$ if the selection is random?
2. How can the concept of a sample space be applied in real-life probability problems?
3. What is the difference between a sample space and an event in probability theory?
4. How do you calculate probabilities of events in a finite sample space?
5. What are complementary events, and what would the complement of choosing $C$ look like?

Tip:

Always ensure the sample space includes all possible outcomes when defining it.