Final answer:
Option (A), The correct probability formula for events A or B that are not mutually exclusive is P(A ∪ B) = P(A) + P(B) - P(A AND B). If they were mutually exclusive, it would be P(A OR B) = P(A) + P(B).
Step-by-step explanation:
The probability formula for events A or B when they are not mutually exclusive is P(A ∪ B) = P(A) + P(B) - P(A AND B). This formula takes into account the possibility that events A and B can occur at the same time.
If A and B were mutually exclusive, their intersection (or the probability of A AND B) would be zero, and the formula would simplify to P(A OR B) = P(A) + P(B).
However, in this case where they may not be mutually exclusive, we subtract P(A AND B) to correct for the fact that we might have counted some outcomes twice.
When events A and B are independent, the multiplication rule can be applied: P(A AND B) = P(A)P(B). But this is not part of the calculation for P(A OR B).
Therefore, the correct option among those provided is:
A) P(A ∪ B) = P(A) + P(B)