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To find the probability of **A or B** occurring, we use the formula for the union of two events:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

### Step 1: Identify values from the diagram
- \( P(A) = \frac{2}{15} + \frac{7}{15} = \frac{9}{15} \)
- \( P(B) = \frac{7}{15} + \frac{4}{15} = \frac{11}{15} \)
- \( P(A \cap B) = \frac{7}{15} \)

### Step 2: Apply the formula
\[
P(A \cup B) = \frac{9}{15} + \frac{11}{15} - \frac{7}{15}
\]

### Step 3: Simplify the expression
\[
P(A \cup B) = \frac{9 + 11 - 7}{15} = \frac{13}{15}
\]

### Final Answer
\[
P(A \cup B) = \frac{13}{15}
\]

Would you like further clarification or a detailed breakdown of any step?

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### 5 Related Questions:
1. What is the formula for the union of three events, \(A \cup B \cup C\)?
2. How does the concept of mutually exclusive events affect this type of calculation?
3. Can the union formula be extended to events with dependent probabilities?
4. How do we calculate \(P(A \cap B^c)\) for the complement of B?
5. What does it mean if \(P(A \cap B) = 0\)?

### Tip:
Always double-check if events are independent or mutually exclusive before applying standard probability formulas!

Find the probability that event A or B will occur.

This problem demonstrates how to calculate the probability of event A or B occurring, using set theory and Venn diagrams. Learn how to apply the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B) with detailed step-by-step explanations. Suitable for Grades 9-12.

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