When two events A and B are mutually exclusive, it means that they cannot occur at the same time. In probability, the special rule of addition for mutually exclusive events states that the probability of either event A or event B occurring is simply the sum of their individual probabilities. This can be expressed mathematically as:
P(A or B) = P(A) + P(B)
For example, if the probability of event A occurring is 0.3 and the probability of event B occurring is 0.5, then the probability of either A or B occurring is:
P(A or B) = 0.3 + 0.5 = 0.8
This rule simplifies the calculation of probabilities when dealing with mutually exclusive events, as it eliminates the need to consider any overlap between the events (since there is none). In contrast, if A and B were not mutually exclusive, we would need to subtract the probability of both events occurring simultaneously, if that were to be a possibility.