Bernoulli Trial

A Bernoulli trial is any experiment in which there can be only two outcomes, usually thought of as a success or failure.

Examples of this can be a coin flip, whether or not you pass a test, or the chances of catching the bus to school.

Assign a 1 to the chance of the event happening, and a 0 to it not happening.

Because discrete distributions have probabilities between 0 and 1, and cannot sum to more than one, a success is defined as p and a failure as 1-p

So the distribution of a Bernoulli trial is seen as

p(x)
0 = 1-p
1 = p