Final answer:
The probability of e or f happening when e and f are not disjoint is calculated using P(e OR f) = P(e) + P(f) - P(e AND f). None of the provided options perfectly matches this formula since the subtraction of the intersection is not included in any option.
Step-by-step explanation:
If e and f are events that are not disjoint, this means there is some overlap between the two events, or in other words, there is a possibility that both can occur at the same time. To calculate the probability of e or f happening (also known as the union of e and f), the correct formula is P(e OR f) = P(e) + P(f) - P(e AND f). Since the events are not disjoint, P(e AND f) is greater than zero, which needs to be subtracted from the sum of the individual probabilities to avoid counting the intersection twice.
Therefore, while the answer is not directly provided among the options, the formula is most closely related to option 2, 'P(e) + P(f)', but it also needs to include the subtraction of their intersection: 'P(e) + P(f) - P(e AND f)'. We can conclude that none of the provided options (1, 2, 3, or 4) is completely correct without this important subtraction to account for the overlap.