Final answer:
Based on the provided probabilities, A and B are mutually exclusive since P(A AND B) = 0. However, the probabilities for A and B are incorrect as they are greater than 1, so we cannot determine their independence.
Step-by-step explanation:
Are the Events A and B Mutually Exclusive or Independent?
Upon examining the given probabilities for events A and B, we determine whether they are mutually exclusive or independent. By definition, mutually exclusive events cannot occur at the same time, implying that if A and B are mutually exclusive, their intersection probability, P(A AND B), would be zero. This is indeed the case here as P(A AND B)=0. Therefore, events A and B are mutually exclusive.
As for independence, for two events to be independent, the probability of their intersection should be equal to the product of their individual probabilities, i.e., P(A AND B) = P(A) x P(B). However, in our case, despite P(A AND B) = 0, the calculation of independence cannot be accurately made as the given values for P(A) and P(B) exceed 1, which violates the basic probability rule that probabilities cannot be greater than 1. Thus, the provided probabilities are erroneous, and we cannot use them to determine independence.
Therefore, based on the information provided and adhering to the rules of probability, we conclude that events A and B are mutually exclusive but we cannot determine if they are independent due to incorrect probability values.