Event/Examples

Examples of Events

Let $\EE$ be the experiment consisting of tossing $2$ coins.

$\Omega = \set {\tuple {\mathrm H, \mathrm H}, \tuple {\mathrm H, \mathrm T}, \tuple {\mathrm T, \mathrm H}, \tuple {\mathrm T, \mathrm T} }$

where $\mathrm H$ denotes heads and $\mathrm T$ denotes tails.

Let $A$ be the subset of $\Omega$ defined as:

$A = \set {\tuple {\mathrm H, \mathrm H}, \tuple {\mathrm H, \mathrm T}, \tuple {\mathrm T, \mathrm H} }$

Let $B$ be the subset of $\Omega$ defined as:

$A = \set {\tuple {\mathrm H, \mathrm H} }$

Then:

$A$ is the event that there is at least one head

$B$ is the event that there are two heads.

Let $\EE$ be the experiment of throwing a standard $6$-sided die.

The sample space of $\EE$ is $\Omega = \set {1, 2, 3, 4, 5, 6}$.

Consider the subset $E \subseteq \Omega$ defined as:

$E = \set {2, 3, 5}$

Then $E$ is the event that the result of $\EE$ is a prime number.

Let $\EE$ be the experiment of throwing a standard $6$-sided die.

The sample space of $\EE$ is $\Omega = \set {1, 2, 3, 4, 5, 6}$.

Consider the subset $E \subseteq \Omega$ defined as:

$E = \set {2, 4, 6}$

Then $E$ is the event that the result of $\EE$ is even.

Let $\EE$ be an experiment whose sample space is defined as $\Sigma = \set {e_1, e_2, e_3}$.

The complete set of events of $\EE$ is:

$\set {\set {e_1}, \set {e_2}, \set {e_3}, \set {e_1, e_2}, \set {e_1, e_3}, \set {e_2, e_3}, \set {e_1, e_2, e_3}, \O}$

The simple events of $\EE$ are:

$E_1 = \set {e_1}, E_2 = \set {e_2}, E_3 = \set {e_3}$

while $\O$ is the trivial event.