https://file.aiquickdraw.com/mathbot/file/1728592828055mcp0sa4l.jpg

Let's analyze the problem presented in the image:

### Problem Breakdown:
1. **Sample Space (All possible outcomes):**
   There are seven balls labeled: \( A, B, C, D, E, F, G \).
   The sample space is simply the set of all these labels, since each one represents a possible outcome when a ball is picked randomly.
   
   So the sample space \( S \) is:
   \[
   S = \{ A, B, C, D, E, F, G \}
   \]

2. **Event of choosing a vowel:**
   Among the seven balls, the vowels are **A** and **E**. Thus, the event of choosing a vowel corresponds to selecting one of these two letters.

   Therefore, the set of outcomes for the event of choosing a vowel is:
   \[
   V = \{ A, E \}
   \]

### Final Answers:
- **Sample space:** \{ A, B, C, D, E, F, G \}
- **Event of choosing a vowel:** \{ A, E \}

Let me know if you'd like further details!

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### Related Questions:
1. How many total outcomes are there in the sample space?
2. What is the probability of randomly selecting a vowel from the bag?
3. How would the sample space change if another ball labeled \( H \) were added?
4. What is the probability of selecting a consonant instead of a vowel?
5. Can you define the complement of the event of choosing a vowel?

**Tip:** When dealing with events in probability, always ensure that you correctly identify whether the outcomes are mutually exclusive or overlapping to avoid confusion.

A bag has seven balls labeled A, B, C, D, E, F, and G. 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 vowel.

Learn how to determine the sample space and outcomes for the event of choosing a vowel from a set of seven balls labeled A, B, C, D, E, F, and G. This problem covers fundamental concepts in probability and set theory, suitable for students in Grades 6-8.

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