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Find the probability that event A OR B will occur

The problem asks for the probability that event \(A\) or \(B\) will occur, represented as \( P(A \cup B) \). This is the probability of the union of events \(A\) and \(B\).

From the Venn diagram in the image, the probabilities associated with each part of the events are:

- Probability of event \(A\) alone: \( \frac{4}{15} \)
- Probability of event \(B\) alone: \( \frac{2}{15} \)
- Probability of the intersection of events \(A\) and \(B\) (i.e., \( A \cap B \)): \( \frac{2}{15} \)

The formula for the union of two events is:

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

Now, using the values from the diagram:

\[
P(A \cup B) = \frac{7}{15} + \frac{4}{15} - \frac{2}{15}
\]

Let me calculate that.The probability that event \(A\) or \(B\) will occur is \( P(A \cup B) = 0.6 \), or \( \frac{6}{10} \) or 60%.

Would you like further details on this or have any questions?

Here are five related questions to deepen your understanding:
1. What is the difference between independent and mutually exclusive events?
2. How would you calculate the probability if events \(A\) and \(B\) were mutually exclusive?
3. What is the probability of \(A \cap B\) based on the diagram?
4. How does the formula for the union of three events differ from the formula for two events?
5. Can the probability of \(P(A \cup B)\) ever be greater than 1?

**Tip:** For overlapping events like these, always remember to subtract the intersection to avoid double-counting shared outcomes.

Find the probability that event A or B will occur.

This problem involves calculating the probability that event A or B will occur using a Venn diagram. The solution utilizes the formula for the union of two events, subtracting the overlap to avoid double-counting. Suitable for Grades 9-12.

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