Final answer:
The union of two events A and B is when either A, B, or both events occur. It's the sum of their probabilities for mutually exclusive events, or a more complex calculation detailed through formulas if the events are not mutually exclusive or are independent.
Step-by-step explanation:
The union of two events A and B is the event that occurs if either event A occurs, event B occurs, or both events occur. It is denoted as A OR B. In probability, this is important in the context of mutually exclusive events and independent events. For mutually exclusive events, which cannot occur at the same time, the probability of their union is simply the sum of their individual probabilities. Specifically, P(A OR B) = P(A) + P(B). However, if A and B are not mutually exclusive, then the probability of their union is P(A) + P(B) - P(A AND B), where P(A AND B) is the probability that both events occur simultaneously. For independent events, the occurrence of one event does not affect the probability of the other. In this case, the probability that both A and B occur is the product of their individual probabilities: P(A AND B) = P(A)P(B).
When analysing conditioned events, such as A GIVEN B (P(A|B)), we're calculating the probability of A occurring given that B has already occurred. A Venn diagram can be a useful visualization for understanding the relationship between two events and their union.