When two events are mutually exclusive then the two events cannot happen at the same time.  For instance, you can't flip a coin and get a heads and a tails at the same time.

Probability (Heads or Tails) = Probability (Heads) + Probability (Tails)   

The events are mutually exclusive.

If the events are not mutually exclusive then the equation looks different:

Probability (A or B) = Probability (A) + Probability (B) + Probability (A and B)

Let's consider independence.  Independence means that the occurrence of one event does not stop or alter the occurrence of the other event.

For instance, choosing a particular marble from a bag does not impact the probability of choosing a particular card from a deck of cards.  These probabilities are independent.