Example of Independent events: Tossing a coin and rolling a dice. The event of the 1st doesn't influence the event of the second and vice versa. If so,
P(A∩B) = P(A).P(B) [if the 1st event is to select A AND B in the 2nd)
Now if the 1st event is to select A OR B in the second:
P(A∪B) = P(A) + P(B)