If E and F are not disjoint​ events, then​ P(E or ​F)equals​________.

If \( E \) and \( F \) are not disjoint events, the probability of \( E \) or \( F \) occurring is given by the **Inclusion-Exclusion Principle**. The formula is:

\[
P(E \cup F) = P(E) + P(F) - P(E \cap F)
\]

So, the probability \( P(E \text{ or } F) \) equals \( P(E) + P(F) - P(E \cap F) \).

This formula adjusts for the fact that \( E \) and \( F \) might overlap (i.e., both events could happen at the same time), so we subtract the probability of their intersection to avoid double-counting.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you calculate \( P(E \cap F) \) if \( E \) and \( F \) are independent events?
2. What is the formula for \( P(E \cup F) \) if \( E \) and \( F \) are mutually exclusive?
3. How does the inclusion-exclusion principle extend to three or more events?
4. What does it mean for events to be disjoint?
5. Can you explain why we subtract \( P(E \cap F) \) in the formula?

**Tip:** When solving probability problems, always check if events are independent, mutually exclusive, or neither. This helps determine the correct formula to use.

Explore the formula for calculating the probability of events E or F occurring together, using the Inclusion-Exclusion Principle. This concept adjusts for overlapping events in probability theory. Suitable for advanced high school students and college-level learners.

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