Which rule states that the probability of at least one event occurring is equal to the probability of one event plus the probability of the other event not occurring?

The correct choice is associated with a principle in probability that helps evaluate different scenarios involving multiple events. This particular rule articulates that the likelihood of at least one of two events happening can be derived from understanding the probabilities of these events separately, specifically considering one event alongside its counterpart that does not occur.

This concept is useful in operations management, especially in risk assessment and decision-making processes, as it allows practitioners to analyze various outcomes based on the interactions of different events. In essence, by calculating the probability of one event and combining it with the understanding of the other’s conditional probabilities, one can effectively determine the overall likelihood of at least one of the considered events taking place.

The other options represent different concepts or rules that might pertain to reliability but do not accurately capture the specific relationship described in the question, which focuses on the interaction of probabilities regarding the occurrence of at least one event versus its alternatives.