Two events A and B are independent if P(A∩B) = P(A) * P(B). The independence of the events A and B means e.g. our calculation of the probability the event A won't change if we will know the event B has occurred. Example: The event A is independent of the event B. This means that if after we will roll die with closing eyes and someone will inform us that number is less than $5$ then our first calculation of the probability of getting an event number won't change. Still will be 1/2. P(A|B) = P(A).