2.2 Bernoulli trials

Simply put, a Bernoulli trial is an experiment that has a random outcome, and there are two and only two possible outcomes. Statisticians often ``normalize'' the outcomes to ``success'' and ``failure'', but these are just two possible labels for the outcomes. Regardless of the labels, a probability $p$ is associated with one label, while $1-p$ is associated with the other label. In the case of ``success'' versus ``failure'', $p$ often represents the probability of ``success''.

For example, when a coin is flipped, the possible outcomes are ``heads'' and ``tails''. We can recast the words, and ask ``what is the probability that we get a heads-up after a flip?'' This way, getting heads-up is now labeled ``success''.

A Bernoulli process is a series of independent but identical Bernoulli trials.