# Sample Space Experiment & Event

__EXPERIMENT:__
Experiment can be of two types:

**Deterministic experiment**and**non-deterministic**or**random experiment**.
An experiment whose outcome is unique is called a

**Deterministic experiment**.
And an experiment whose outcome is not unique and cannot be calculated in advance,
but is one of the set of possible outcomes, then it is called a

**random experiment**.

__SAMPLE SPACE:__
The set of all possible outcomes of a random experiment is called the

**sample space**. Sample space is denoted by**S**
For example, when we toss a coin there can be two possible outcomes, head or tail.
So the sample space of this experiment will be, S = {H, T}

A few more examples of sample space are:

In the experiment of throwing a pair of dice, S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),...... (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

In the experiment of tossing two coins simultaneously,

S = {HH, HT, TH, TT}

A few more examples of sample space are:

In the experiment of throwing a pair of dice, S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),...... (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

In the experiment of tossing two coins simultaneously,

S = {HH, HT, TH, TT}

__EVENT:__
An

**event**is a subset of the sample space. It is denoted by**E**. For example, {a tail} in the experiment of tossing a coin is an event. There are two types of events:**Simple event**and**compound event**.
If an event has only one element of the sample space then it is called a

**simple event**.
For example, in S = {2, 5, 6, 9} if the event is set of elements greater than 6
then E = {9} is a

**simple event**.
If an event has more than one elements of the sample space then it is called a

**compound event**. For example, in the experiment of tossing two coins together the sample space will be, S = {HH, HT, TH, TT} if the event has two of the same side then E = {HH, TT} is a**compound event**.**Online Sample Space, Experiment, Event Help:**

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