Final answer:
To check if two events are mutually exclusive, calculate the probability of both events occurring together (P(A AND B)).
Step-by-step explanation:
To determine whether two events are mutually exclusive in mathematics, you need to consider the probability of both events happening at the same time. If event A and event B are mutually exclusive, the probability of A AND B occurring together, denoted as P(A AND B), is equal to zero. This means there are no outcomes that both events share.
Consider, for example, a sample space S representing all possible outcomes of an experiment. If you have event A and event B, you can find out if these events are mutually exclusive by calculating the intersection of A and B, which are the outcomes they share. If A AND B equals {}, meaning there are no common outcomes, they are mutually exclusive, and the probability is 0.
Another aspect to consider is that if A and B are mutually exclusive, then the probability of A or B occurring, denoted as P(A OR B), is the sum of the probabilities of each event occurring independently since there's no overlap. Thus, P(A OR B) = P(A) + P(B).