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To solve the problem of finding the probability that event \(A\) or \(B\) will occur, denoted as \(P(A \cup B)\), we use the formula for the union of two events:

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

### From the Venn diagram:
- \(P(A)\), the probability of event \(A\), is given by adding the probabilities inside circle \(A\), which is \( \frac{4}{15} + \frac{1}{15} = \frac{5}{15} \).
- \(P(B)\), the probability of event \(B\), is given by adding the probabilities inside circle \(B\), which is \( \frac{2}{15} + \frac{1}{15} = \frac{3}{15} \).
- \(P(A \cap B)\), the probability that both \(A\) and \(B\) occur (the overlap), is \( \frac{1}{15} \).

Now apply the formula:

\[
P(A \cup B) = \frac{5}{15} + \frac{3}{15} - \frac{1}{15}
\]
\[
P(A \cup B) = \frac{7}{15}
\]

Thus, the probability that event \(A\) or \(B\) will occur is:

\[
P(A \cup B) = \frac{7}{15}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the probability of event \(A\) happening but not \(B\)?
2. How does the formula for \(P(A \cup B)\) change if the events are mutually exclusive?
3. What is the probability that neither event \(A\) nor event \(B\) will occur?
4. Can you extend this probability concept to three events?
5. How is the complement rule applied in this case?

### Tip:
In probability, always remember to subtract the overlap \(P(A \cap B)\) when calculating \(P(A \cup B)\), to avoid double-counting.

Find the probability that event A or B will occur.

Learn how to find the probability of event A or B occurring with the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). This problem uses a Venn diagram and covers key probability concepts. Suitable for students in Grades 9-12.

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