# B What exactly is an 'exhaustive event'?

#### Richard_Steele

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
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#### tnich

Homework Helper
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

#### Richard_Steele

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

#### FactChecker

Gold Member
2018 Award
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

#### WWGD

Gold Member
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.

#### Mark44

Mentor
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

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