Is an example of the compliment rule being applied to mutally exclusive events?

Yes, the complement rule can be applied to mutually exclusive events. For example, if you have two mutually exclusive events, A and B, the probability of either event occurring is given by P(A or B) = P(A) + P(B). The complement rule states that the probability of the complement of an event, such as neither A nor B occurring, is 1 minus the probability of A or B, or P(not A and not B) = 1 - P(A or B). Thus, the complement rule effectively helps calculate the probabilities related to mutually exclusive events.