Mutually exclusive events are events that can not happen at the same time. For example, you can not sit down and stand up at the same time. These two events are mutually exclusive.
For event A and B, the probability of their union is the sum of the probabilities of the events.
A and B, cannot have any elements in common, or P(A∩B)= 0 , it means probability of happening at same time is 0.
When two events are said to be independent of each other, it means the probability that one event occurs is in no way affecting the probability of the other event occurring. An example of two independent events is rolling a die and flipping a coin.
Two events, A and B are independent if and only if:
P(A and B)=P(A)×P(B)
For two events, A and B, independence means that knowing the outcome of B will not affect the probability of A.
In conclusion , mutually exclusive events are almost depended on each other for one to happen, whereas independent events can happen without the effect of other.