Definition:Bernoulli Trial

Definition
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.

Also defined as
Some sources insist that $0 < p < 1$, but it can be useful in certain circumstances to include the condition when the outcome is certainty.