If two events are mutually exclusive then they do not occur simultaneously, hence they are not independent.

Yes, there is relationship between mutually exclusive events and independent events.

Let's clarify that mutually exclusive events do not share any sample points with each other, so they cannot occur at the same time. Thus, if event A and event B are mutually exclusive, they are actually inextricably DEPENDENT on each other because event A's existence reduces Event B's probability to zero and vice-versa.

Mutually exclusive events are necessarily also dependent events because one's existence depends on the other's non-existence.

That being said, I don't believe a similar relationship can be drawn from the other direction. Dependent events are not necessarily mutually exclusive; they can share sample points while influencing each other's probabilities in other ways.

For example, Flower A and Flower B can grow in the same area, but perhaps Flower A's growth impedes Flower B's growth, so the probability of Flower B growth changes given Flower A's existence; they share points and are dependent one each other, showing that you cannot assume mutual exclusivity from dependence.

we know that in the independence P(A,B)= P(A)P(B), besides we know that two events are disjoint (mutually exclusive) only if P(A,B)=0, so taking the two assumptions we can say that if P(A) and P(B) are different from zero, hence independent events are not disjoint events.

Rachel Xian is right. When thinking about mutual exclusivity and independence, a counter-intuitive result emerges: mutually exclusive events must be dependent events . If we know the student is on-time to class on that day, there is zero chance that the students is late! If A is the event that Maria is on-time to class today and B is the event that Maria is late to class today, events A and B are both mutually exclusive and dependent. Clearly the events are mutually exclusive, and it is also clear they are dependent because if A (Maria is on-time) occurs, we know with certainty that B (she is late) did not occur.