# What exactly is an 'exhaustive event'?

• B
• Richard_Steele
In summary, an exhaustive event is a comprehensive evaluation of all possible outcomes in a given situation. It differs from a non-exhaustive event which may have missing or incomplete information. Examples of exhaustive events include scientific experiments and surveys that consider all possible variables and responses. Considering exhaustive events is important in scientific research as it reduces the risk of bias and allows for a more thorough understanding of the subject. To ensure an event is exhaustive, careful consideration of all possible outcomes, thorough planning, and a diverse and knowledgeable team are necessary.
Richard_Steele
TL;DR Summary
Want to know exactly what an exhaustive event is. A little bit confused about "one of them will occur during the conduct of an experiment".
Summary: Want to know exactly what an exhaustive event is. A little bit confused about "one of them will occur during the conduct of an experiment".

Hi there, I open this thread because I am a little bit confused about what an 'exhaustive event' is. I have been reading some websites and watching a video in youtube and I get some idea, but I don't fully understand the concept at 100%. So I am going to explain what I understand at this moment.

Given a sample space (for example, a dice): S={1, 2, 3, 4, 5, 6}
I get two subsets, for example:
A={1, 2, 3}
B={4, 5, 6}

So, A and B are exhaustive events because when I perform an experiment the event must belong to A or to B subset. Also, A and B are exhaustive events because if we put together A and B, the form a complete sample space.

Is my understanding right?
Thanks.

tnich
Richard_Steele said:
Summary: Want to know exactly what an exhaustive event is. A little bit confused about "one of them will occur during the conduct of an experiment".

Hi there, I open this thread because I am a little bit confused about what an 'exhaustive event' is. I have been reading some websites and watching a video in youtube and I get some idea, but I don't fully understand the concept at 100%. So I am going to explain what I understand at this moment.

Given a sample space (for example, a dice): S={1, 2, 3, 4, 5, 6}
I get two subsets, for example:
A={1, 2, 3}
B={4, 5, 6}

So, A and B are exhaustive events because when I perform an experiment the event must belong to A or to B subset. Also, A and B are exhaustive events because if we put together A and B, the form a complete sample space.

Is my understanding right?
Thanks.
You've got it right. Sets ##A## and ##B## are collectively exhaustive iff ##A\cup B = U## where ##U## is the set of all possible events. A concept that goes along with this is mutually exclusivity. Sets ##A## and ##B## are mutually exclusive iff ##A\cap B = \phi##. So you often see the phrase "mutually exclusive and collectively exhaustive".

Richard_Steele
tnich said:
You've got it right. Sets ##A## and ##B## are collectively exhaustive iff ##A\cup B = U## where ##U## is the set of all possible events. A concept that goes along with this is mutually exclusivity. Sets ##A## and ##B## are mutually exclusive iff ##A\cap B = \phi##. So you often see the phrase "mutually exclusive and collectively exhaustive".
Thanks very much for the answer. The first descriptions about exhaustive events were a little bit confused, but now thanks to your explanation I better understand the concept. Thank you very much!

Klystron and berkeman
Just a bit of terminology knit-picking:
The only "exhaustive event" would be the universal set, U. Other than that, it is a collection of events that are exhaustive. So you can talk about an exhaustive set (of events) or an exhaustive collection, but you should not talk about a single exhaustive event unless you are talking about U.

Mark44
It is , as I understand it too,covering all possibilities. Flip a coin, barring the coin landing on its side, it will land heads or tails.

FactChecker said:
The only "exhaustive event" would be the universal set, U. Other than that, it is a collection of events that are exhaustive.
I agree. Only a collection of events (or the universal set) can be termed exhaustive. The term "exhaustive" is used because such events exhaust, or use up, all of the possibilities that can arise. Besides the "head" and "tail" events that @WWGD mentioned, for a fair, six-sided standard die, the only possible events are that the face showing has one, two, three, four, five, or six pips. Not included are the virtually impossible events that the thrown die balances on one edge or on one corner.

Klystron

## 1. What is an exhaustive event?

An exhaustive event is an event that includes all possible outcomes and leaves no room for any other outcome. It is a complete and comprehensive event that covers all possible scenarios.

## 2. How is an exhaustive event different from a non-exhaustive event?

A non-exhaustive event is an event that does not cover all possible outcomes and leaves room for other outcomes to occur. It is not comprehensive and may not include all possible scenarios.

## 3. Can you give an example of an exhaustive event?

An example of an exhaustive event is flipping a coin. The possible outcomes are either heads or tails, and no other outcome is possible. This covers all possible scenarios and is therefore an exhaustive event.

## 4. Why is it important to understand exhaustive events?

Understanding exhaustive events is important in various fields, such as statistics, probability, and decision-making. It allows for accurate analysis and prediction of outcomes, and helps in making informed decisions.

## 5. How can we identify an exhaustive event?

An exhaustive event can be identified by listing all possible outcomes and ensuring that no other outcome is possible. It should cover all possible scenarios and leave no room for any other outcome.

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