Difference Between Mutually Exclusive and Independent Events

The difference between mutually exclusive and independent events is: a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time whereas independent event occurs when one event remains unaffected by the occurrence of the other event.

An independent event is termed as an event that occurs without being affected by other events. This is termed as an independent event. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two. Suppose an event does not take place that does not stop other events from happening. The types of events in Probability will give you an overview of the different types of events that occur.

Mutually exclusive events: 

• When the occurrence is not simultaneous for two events then they are termed as Mutually exclusive events.
• The non-occurrence of an event will end up in the occurrence of an event.
• The mathematical formula for mutually exclusive events can be represented as P(X and Y) = 0
• The sets will not overlap in the case of mutually exclusive events.

Independent events

• When the occurence of one event does not control the happening of the other event then it is termed as an independent event.
• There is no influence of an occurrence with another and they are independent of each other.
• The mathematical formula for independent events can be defined as  P(X and Y) = P(X) P(Y)
• The sets will overlap in the case of independent events.