Theorem of total probability : If A and B two mutually non-exclusive events associated with random experiment then P(A+B)=P(A∪B)=P(A)+P(B)−P(A∩B) Proof : Consider the ven diagram in which A and B are two subsets sample spaces shaded portion represents the set A∩B Let r,s and t be the number of elementary events in set A,B, and A∩B and n be the total number of elements of S. The number of elementary events in the set A∪B representing the event A and B is equal to =r+s−t. P(A∪B)=r+s−tn=rn+sn−tn =P(A)+P(B)−P(A∩B) By definition of probability.