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.
Also, read: Independent Events
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?
What are independent events?
How to represent mutually exclusive and independent events?
The mathematical formula for independent events can be represented as P(A and B) = P(A) P(B)
For the same experiment , i e in the same sample space, if Event A occurs, it reduces the sample space of Event B from U to A
If Event A does not occur ,that also reduces the sample space of B to A’s compliment, (U – A).
Either way the probability of B will depend on the result of A.
Two Events can be independent only if they are for different experiments.
So, two events can be mutually exclusive and dependent too sometime right?
It’s helpful to think about this in terms of sample space.
Say we have events A and B , both being subsets of sample space S.
Then if at one time only A or B can occur then the events are mutually exclusive.
Now, say we have two events A and B where A is a subset of sample space S1 and B is a subset of a different sample space S2.
Clearly, if A occurs then this won’t have any effect on occurrence of B and vice versa. Therefore A and B are independent events.