Difference Between Mutually Exclusive and Independent Events

Events occur as a result of experiments that are usually termed random or uneven.

During a course of an experiment, the events are always kept tabs on by the mathematical function of probability.

In an experiment, many events have their probabilities measured such as mutually exclusive, independent, dependent, simple, or compound.

Mutually Exclusive vs Independent Events

The main difference between mutually exclusive and independent events is that mutually exclusive events tend to not let more than one event happen during a single period whereas, in the case of independent events, there are probabilities of many numbers of events taking place at the same time or one after the other.

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Mutually exclusive as the name suggests gives an event type where the occurring event can’t be more than one at a given possible moment.

This means that the events that happen are all individual and unique at all times and no recurring ones could be expected.

Given a particular time limit and within that, there can’t be more than a single experimental occurring giving rise to a mutually exclusive event.

Independent events are what normally people mean once they refer to any event.

In this type of probability, more than one or even more than any number of events can take place without affecting another event that might have been taking place at the same time as the one in reference.

There are no limits in the number of occurrences that might take place together within a single experimental event.

Comparison Table Between Mutually Exclusive and Independent Events

Parameters of ComparisonMutually Exclusive EventsIndependent Events
Do One Event Influence Another in the Same Environment?YesNo
FormulaP(A and B) = 0P(A and B) = P(A) P(B)
Nature of Venn DiagramThe circles don’t overlapCircles overlap
Simultaneous OccurrencesNoYes
Other NamesMany such as disjoint events, etcNot much

What is Mutually Exclusive Event?

Mutually exclusive events are often called disjoint events.

It always means an individual occurrence that isn’t accompanied by any other happening at the same time.

An event happening during a selected period has no chance to influence another happening along with it.

This is because such an event is always a single one. No two events are happening together.

But that event for certain influences the experimental surrounding around itself.

This technically means that there is no experimental occurrence happening simultaneously.

It defies some laws that people might see as general common sense.

In certain scenarios, an event being mutually exclusive might seem impossible as those events need to be happening together at the same time.

It is rare to have an event be categorized under the probability of being mutually exclusive.

The most common example of such an event is the tossing of a coin.

During a single toss, there is a probability of the toss turning out to be either head or tail.

Never can a single toss result in both heads or tails. Of course, the coin can always land vertically without falling on one side.

But such cases are rare and those events are categorized to a different probability factor.

This clearly shows that the occurrence of an individual event makes the happening of another event in the same period impossible.

In mutually exclusive events, all happenings are unique and have control over themselves.

It can’t exert a controlling element over another event.

What is Independent Event?

As the name suggests, an individual event holds no responsibility for the pattern of another event happening around it.

Two or more experimental occurrences can happen together, but in an independent event, they don’t affect each other.

This probability is the most commonly seen event type around us as most environmental occurrences happen irrespective of another.

Independent events don’t influence its surrounding to change to accommodate the event.

Neither does an independent hold any influence over other events taking place in its same environment.

This influence would be impossible to happen as all events in the probability of an independent event are naturally separated from each other.

The easiest example of an independent event is that of two coins being tossed simultaneously beside each other.

The probability of heads and tails each are two whereas the probability of one each is also the very same.

This clearly shows that one coin toss doesn’t hinder the probability of the coin toss happening at the same time beside it.

Any event happening independently has the upper hand to let all other events happening around it independently too.

This added advantage is also why most probability factors around us are also independent.

If in a sack filled with colored balls and two people are picking up a ball each, either can pick the same color or different ones.

This is all a magnificent mathematical probability showing relative effects of events.

Main Differences Between Mutually Exclusive and Independent Events

  1. While mutually exclusive events influence the occurrence of any other event if it takes place in the same environment independent events don’t have such an influence.
  2. Independent events can happen at the same time whereas mutually exclusive events can’t happen simultaneously.
  3. In the Venn diagram for independent events, the circles overlap while in that for mutually exclusive events, they don’t overlap.
  4. While the mathematical formula for mutually exclusive events equates to zero, that if independent events don’t and are always in a probability of two events.
  5. Mutually exclusive events don’t occur at one for while independent events do.

Conclusion

Independent events and mutually exclusive events are never the same.

Even though they indicate the probabilities of occurrences the mathematical factor indicates different things.

If an event is categorized as a mutually exclusive event, then there is no chance of it being called an independent event.

This can be true the other way around also.

The mathematical formulae indicate the probability and functions of the events.

While mutually exclusive events have got many other names that are commonly used, independent events don’t have such names.

The most common event in nature is an independent event.

To have a mutually exclusive event as the common natural probability, there would be lots of restrictions in nature.

References

  1. https://www.stat.auckland.ac.nz/~iase/publications/icots2/Kelly.Zwiers.pdf
  2. https://www.tandfonline.com/doi/abs/10.1080/00031305.1987.10475443
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