If E and F are two disjoint events with P(E) = 0.11 and P(F) = 0.36, what is P(E ∪ FC)? (Enter answer as a decimal with at least 2 correct decimal places)

Given:

- \( P(E) = 0.11 \)
- \( P(F) = 0.36 \)
- \( E \) and \( F \) are disjoint events (i.e., \( P(E \cap F) = 0 \)).

We need to find \( P(E \cup F^c) \), where \( F^c \) is the complement of event \( F \).

### Step 1: Calculate \( P(F^c) \)
By the definition of complement:
\[
P(F^c) = 1 - P(F)
\]
\[
P(F^c) = 1 - 0.36 = 0.64
\]

### Step 2: Calculate \( P(E \cup F^c) \)
The formula for the union of two events is:
\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
Here, \( A = E \) and \( B = F^c \). Since \( E \) and \( F \) are disjoint, \( E \) and \( F^c \) are also disjoint because \( E \cap F = 0 \), so \( E \) does not overlap with \( F^c \). Therefore:
\[
P(E \cap F^c) = 0
\]

Thus, the formula simplifies to:
\[
P(E \cup F^c) = P(E) + P(F^c)
\]
\[
P(E \cup F^c) = 0.11 + 0.64 = 0.75
\]

### Final Answer:
\[
P(E \cup F^c) = 0.75
\]

Would you like any further explanation or details on this?

Here are 5 related questions for further exploration:
1. How would the calculation change if \( E \) and \( F \) were not disjoint?
2. What is \( P(F \cap E^c) \)?
3. How do we calculate \( P(E^c \cup F) \)?
4. If \( P(E \cap F^c) \) were nonzero, how would the solution change?
5. How does the inclusion-exclusion principle apply to non-disjoint events?

**Tip:** Always confirm whether events are disjoint or independent, as it significantly affects the calculation of unions and intersections.

Learn how to calculate P(E ∪ F^c) for two disjoint events E and F with probabilities P(E) = 0.11 and P(F) = 0.36. This problem uses key probability formulas and is suitable for students in Grades 9-12.

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