https://file.aiquickdraw.com/mathbot/file/1726207526493qx4d433g.jpg

The image contains a set of probability-related questions and a Venn diagram with two events, \( A \) (Red) and \( B \) (Blue), related to a survey of learners' favorite colors. Here's an overview of the key details:

### Venn Diagram Information:
- **\( R \)**: Represents the universal set (total = 100 learners surveyed).
- **Event \( A \)** (Red): Contains a total of \( 28 + 19 = 47 \) learners.
- **Event \( B \)** (Blue): Contains a total of \( 19 + 42 = 61 \) learners.
- **Intersection \( A \cap B \)** (both Red and Blue): Contains 19 learners.
- **Complement areas**:
    - Only Red (\( A \setminus B \)): 28 learners.
    - Only Blue (\( B \setminus A \)): 42 learners.
    - Outside both sets (neither Red nor Blue): 11 learners.

### Questions Overview:
1. **1.1** to **1.4**:
   - These questions ask about events being mutually exclusive, exhaustive, complementary, and to write down the value of \( P(S) \).

2. **2.1** to **2.4**:
   - These involve calculating probabilities, drawing a Venn diagram, and verifying mutually exclusive events, given \( P(A) = 0.6 \), \( P(B) = 0.5 \), and \( P(A \cap B) = 0.3 \).

Would you like me to solve one specific question or go through the entire problem set in order?

A class conducted a survey of 100 learners on their favorite color. Event A represents learners who chose red, and Event B represents learners who chose blue. The Venn diagram shows the results, and the questions ask about events being mutually exclusive, exhaustive, complementary, and probabilities.

Solve a probability problem involving 100 students choosing their favorite colors (red or blue) using Venn diagrams. Understand the concepts of mutually exclusive, exhaustive, and complementary events, along with calculating probabilities.

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