Question

explain addition theorem in probability

Answer 1

The addition theorem in the Probability concept is the process of determination of the probability that either event ‘A’ or event ‘B’ occurs or both occur. The notation between two events ‘A’ and ‘B’ the addition is denoted as '∪' and pronounced as Union. The result of this addition theorem generally written using Set notation, P (A ∪ B) = P(A) + P(B) – P(A ∩ B), Where, P (A) = probability of occurrence of event ‘A’ P (B) = probability of occurrence of event ‘B’ P (A ∪ B) = probability of occurrence of event ‘A’ or event ‘B’. P (A ∩ B) = probability of occurrence of event ‘A’ or event ‘B’. Addition theorem probability can be defined and proved as follows: Let ‘A’ and ‘B’ are Subsets of a finite non empty set ‘S’ then according to the addition rule P (A ∪ B) = P (A) + P (B) – P (A). P (B), On dividing both sides by P(S), we get P (A ∪ B) / P(S) = P (A) / P(S) + P (B) / P(S) – P (A ∩ B) / P(S) (1). If the events ‘A’ and ‘B’ correspond to the two events ‘A’ and ‘B’ of a random experiment and if the set ‘S’ corresponds to the Sample Space ‘S’ of the experiment then the equation (1) becomes P (A ∪ B) = P (A) + P (B) – P (A). P (B), This equation is known as the addition theorem in probability. Here the event A ∪ B refers to the meaning that either event ‘A’ or event ‘B’ occurs or both may occur simultaneously. If two events A and B are Mutually Exclusive Events then A ∩ B = ф, Therefore P (A ∪ B) = P (A) + P(B) [since P(A ∩ B) = 0], In language of set theory A ∩ B̅ is same as A / B.