the first sub question is asking for P(AUD), the second one is P(EUB), third is P(DUE) and then P(CUF)

Sure, let's denote the events as follows to clarify and solve for the probabilities:

1. \( P(A \cup D) \) 
2. \( P(E \cup B) \)
3. \( P(D \cup E) \)
4. \( P(C \cup F) \)

### 1. \( P(A \cup D) \)

Using the formula for the probability of the union of two events:
\[ P(A \cup D) = P(A) + P(D) - P(A \cap D) \]

### 2. \( P(E \cup B) \)

Using the same formula:
\[ P(E \cup B) = P(E) + P(B) - P(E \cap B) \]

### 3. \( P(D \cup E) \)

Similarly:
\[ P(D \cup E) = P(D) + P(E) - P(D \cap E) \]

### 4. \( P(C \cup F) \)

And for the last one:
\[ P(C \cup F) = P(C) + P(F) - P(C \cap F) \]

### Steps to Calculate

1. **Identify the individual probabilities:** \( P(A), P(D), P(E), P(B), P(C), P(F) \)
2. **Identify the intersection probabilities:** \( P(A \cap D), P(E \cap B), P(D \cap E), P(C \cap F) \)
3. **Apply the formula:** Substitute these values into the union probability formula.

Please provide the specific probabilities of these events and their intersections so I can compute the exact values for you.

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Do you want detailed explanations or have any questions about the process? Here are some related questions that might help expand your understanding:

1. How do you calculate the intersection of two probabilities?
2. What is the difference between union and intersection in probability?
3. How does the principle of inclusion-exclusion apply to probability?
4. Can you explain with a Venn diagram how the union of two events is calculated?
5. How would the formulas change if the events were mutually exclusive?

**Tip:** Remember that for mutually exclusive events, the intersection probability \(P(A \cap B)\) is zero, simplifying the union formula to \(P(A \cup B) = P(A) + P(B)\).

The first sub question is asking for P(AUD), the second one is P(EUB), third is P(DUE) and then P(CUF)

Learn how to calculate the probability of the union of multiple events using the inclusion-exclusion principle. This problem breaks down the calculations for P(A ∪ D), P(E ∪ B), P(D ∪ E), and P(C ∪ F), with clear formulas and steps. Suitable for students in Grades 10-12.

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