additionsreglerna

The additionsreglerna, often translated as the addition rules, are fundamental principles in probability theory used to calculate the probability of the union of two or more events. Specifically, the rule for two events, A and B, states that the probability of A or B occurring, denoted as P(A ∪ B), is equal to the sum of their individual probabilities minus the probability of both occurring simultaneously. This is expressed by the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability of the intersection of events A and B.

This formula accounts for the fact that if events A and B are not mutually exclusive, meaning they can occur at the same time, simply adding P(A) and P(B) would double-count the outcomes where both events are present. Subtracting P(A ∩ B) corrects for this overlap. If the events are mutually exclusive, meaning they cannot occur at the same time, then P(A ∩ B) is zero, and the formula simplifies to P(A ∪ B) = P(A) + P(B). The additionsreglerna can be extended to more than two events, though the formulas become more complex, involving the probabilities of intersections of all combinations of events. These rules are crucial for solving a wide range of probability problems, from simple coin toss scenarios to complex statistical analyses.