# 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 $\left\{h,t\right\}$ .

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.

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