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.