Final answer:
An interaction between two events, A and B, implies that they are dependent since the occurrence of one affects the probability of the occurrence of the other. Independence would require that P(A AND B) = P(A)P(B), which isn't the case if there's an interaction.
Step-by-step explanation:
When discussing the independence of two events, A and B, in probability, we are referring to whether the occurrence of one event affects the likelihood of the occurrence of the other. Specifically, two events are considered independent if the probability of both events occurring together is equal to the product of their individual probabilities, expressed mathematically as P(A AND B) = P(A)P(B).
If we can confirm that P(A AND B) = P(A)P(B), then we can conclude that events A and B are independent. If this condition does not hold, then A and B are considered dependent. Without further information to indicate that they are independent, we should assume that A and B are dependent until proven otherwise.
Applying this rule, if an interaction between A and B is observed, it implies that the occurrence of A in some way affects the probability of B occurring, or vice versa. This is indicative of a dependency between A and B, rather than an independence