# How do you determine the theoretical probability of rolling a five on a die?

##### 1 Answer

The *probability* of any *event* is based on given probabilities of *elementary events* and a composition of our *event* as a set of *elementary events*.

If we know the probabilities of *elementary events* and a composition of our *event*, the probability of our *event* is a sum of probabilities of all *elementary events* that comprise it.

In case of a die, the elementary events are numbers rolled on this die. The so-called "fair" die has all its 6 numbers equally probable. Since the total probability always equals to 1, the probability of each *elementary event* (rolling each number from 1 to 6) equals to

An *event* offered in the problem, "rolling a five on a die", contains only one *elementary* event - number 5, whose probability we know as being equal to

Just as an example, an *event* "Rolling a number that is less than five" contains 4 different *elementary events* - rolling 1, 2, 3 or 4. Each of them has a probability *elementary events* comprising our *event*, that is the *probability* of our event, is