Explain addition theorem in probability, with example.

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’.