 # 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 example of a mutually exclusive event is when a coin is a tossed and there are two events that can occur, either it will be a head or a tail. Hence, both the events here are mutually exclusive. But if we take two separate coins and flip them, then the occurrence of Head or Tail on both the coins are independent to each other.

There are quite a few different events that occur in Probability such as Simple, Compound, Independent, Dependent and Mutually Exclusive. It is important to know what causes these events to be different from one another.

## What is the Difference between Mutually exclusive events and Independent events?

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.

Difference between Mutually exclusive and independent events
Mutually exclusive events Independent events
When the occurrence is not simultaneous for two events then they are termed as Mutually exclusive events. When the occurence of one event does not control the happening of the other event then it is termed as an independent event.
The non-occurrence of an event will end up in the occurrence of an event. There is no influence of an occurrence with another and they are independent of each other.
The mathematical formula for mutually exclusive events can be represented as P(X and Y) = 0 The mathematical formula for independent events can be defined as  P(X and Y) = P(X) P(Y)
The sets will not overlap in the case of mutually exclusive events. The sets will overlap in the case of independent events.

Thus, these are the major differences between Mutually exclusive and independent events.

## Frequently Asked Questions on the Difference between Mutually Exclusive and Independent Events

### What is a mutually exclusive event?

When two events do not occur simultaneously then they are termed as Mutually exclusive events.

### What are independent events?

When the occurence of one event will not control the happening of the other event in an experiment then it is termed as an independent event.

### How to represent mutually exclusive and independent events?

If A and B are two events, then mutually exclusive is represented by: P(A and B) = 0.
The mathematical formula for independent events can be represented as P(A and B) = P(A) P(B)