# Sample Space

A
**
sample space
**
is the set of all possible outcomes of a random experiment. When you toss a coin, there are only two possible outcomes-heads
$\left(h\right)$
or tails
$\left(t\right)\text{\hspace{0.17em}}$
so the sample space for the coin toss experiment is
$\{h,t\}$
.

Any
subset
of possible outcomes for an experiment is known as an
**
event
**
. When an event is a single element of the sample space, it may be called a
**
simple event
**
.
$\left\{h\right\}$
and
$\left\{t\right\}$
are simple events for the coin toss experiment.

**
Example :
**

For the rolling of a single die, specify $\left(1\right)\text{\hspace{0.17em}}$ the sample space of the experiment; $\left(2\right)\text{\hspace{0.17em}}$ the event that a number less than $4$ results and $\left(3\right)\text{\hspace{0.17em}}$ the event that an even number results.

$\begin{array}{l}\left(1\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\{1,2,3,4,5,6\}\\ \left(2\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\{1,2,3\}\\ \left(3\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\{2,4,6\}\end{array}$