Final answer:
Without specific data on the probability of being hit by any major hurricane, we cannot accurately calculate the probabilities for part (a) and (b) of the question. The complement rule would be applied if such data were provided.
Step-by-step explanation:
To calculate the probability that the state will not be hit by any major hurricanes in a single year, we require specific data about past occurrences or a given probability. However, if we assume that the relative frequency of direct hits by a category 4 hurricane is given to be 0.0768, and we take this as a proxy probability, then we would use the complement rule. The complement rule states that the probability of the complement event (not being hit by a major hurricane) is 1 minus the probability of the event occurring. Therefore:
Probability (not hit by a major hurricane) = 1 - Probability (hit by a major hurricane).
However, without knowing the specific probability of being hit by any major hurricane (all categories included), we cannot give a numerical answer. For part (b), the probability of being hit by at least one major hurricane would be the opposite of not being hit, which again requires the initial probability to calculate.
To determine if these probabilities are unusual, one would compare them to a threshold or historical data. Typically, a probability is considered unusual if it is less than 5% or greater than 95%.