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