All cases in which manifestations have exactly two characteristics follow a Bernoulli distribution.

Typical examples are coin flip or medical treatment, which works or not.

Let X be a random variable with and a probability function of

Written in a compact way:

The expected value is defined through:

In case of having a series of Bernoulli events, we are having a Binomial distribution. For example, the out come of a repeated coin flip follows a Binomial distribution.