Definition:Bernoulli Trial

Definition
A Bernoulli trial is an experiment whose sample space has two elements, which can be variously described, for example:


 * Success and failure;


 * True and False;


 * $1$ and $0$;


 * The classic heads and tails.

Formally, a Bernoulli trial is modelled by a probability space $\left({\Omega, \Sigma, \Pr}\right)$ such that:


 * $\Omega = \left\{{a, b}\right\}$


 * $\Sigma = \mathcal P \left({\Omega}\right)$

where $0 \le p \le 1$.
 * $\Pr \left({a}\right) = p, \Pr \left({b}\right) = 1 - p$

That is, $\Pr$ obeys a Bernoulli distribution.