Definition:Bernoulli Trial

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.