# Probability Space

## Probability Space

Set of events in a random experiment in which we attributed a probability to each event.

A probability space is a set of event-probability pairs. The probability space is a synonym for probability triple.

### Example

Consider the random experiment of rolling a fair die with four faces (tetrahedron) numbered 1 to 4 and observing the result on the bottom face.

The set of possible outcomes is $$\textrm{U}$$ = {1, 2, 3, 4}.

The probability space of this event is:

$$\left\{ \left( \left\{ 1\right\} ,\dfrac {1} {4}\right), \space \left( \left\{ 2\right\} ,\dfrac {1} {4}\right), \space \left( \left\{ 3\right\} ,\dfrac {1} {4}\right), \space \left( \left\{ 4\right\} ,\dfrac {1} {4}\right) \right\}$$