What is the formula for the probability of A or B when A and B are not mutually exclusive?

When considering the probability of events A or B occurring, especially when they are not mutually exclusive, it is important to account for the overlap between the two events. The correct formula to use in this scenario is P(A) + P(B) - P(A and B).

This makes sense because if you simply add P(A) and P(B), you would double-count the probability of the event where both A and B occur (which is represented by P(A and B)). By subtracting P(A and B), you adjust for this overlap, ensuring the total probability accurately reflects the likelihood of either event happening.

In contrast, other options do not properly account for this overlap. For instance, adding P(A) and P(B) would lead to an incorrect total probability when A and B can occur together. The other formulas present the probabilities in a way that either ignores the possibility of their intersection entirely or misrepresents the relationship between the events. Thus, the formula P(A) + P(B) - P(A and B) is the appropriate choice for non-mutually exclusive events.