The simplest kind of random situation is one in which there are only two possible outcomes that can be given the names 'success' and 'failure'. This is called a Bernoulli trial.

A few commonly encountered distributions arise from a series of independent Bernoulli trials. This chapter finds their probability functions and derives their means and variances.

The Bernoulli random variable is based on a single Bernoulli trial and is defined to be 1 if a success occurs and 0 otherwise.

The binomial distribution is a generalisation of this and describes the number of successes in n such independent trials.

A geometric distribution describes the number of trials until the first success is observed. The negative binomial distribution generalises this and is the distribution of the number of trials until the k'th success.