\begin{definition}[Definition:Bernoulli Trial]
A '''Bernoulli trial''' is an experiment whose sample space has two elements, which can be variously described, for example, as:
:'''Success''' and '''failure'''
:'''True''' and '''False'''
:$1$ and $0$
:the classic '''heads''' and '''tails'''.
Formally, a '''Bernoulli trial''' is modelled by a probability space $\struct {\Omega, \Sigma, \Pr}$ such that:
:$\Omega = \set {a, b}$
:$\Sigma = \powerset \Omega$
:$\map \Pr a = p, \map \Pr b = 1 - p$
where:
:$\powerset \Omega$ denotes the power set of $\Omega$
:$0 \le p \le 1$
That is, $\Pr$ obeys a Bernoulli distribution.
\end{definition}