Probability corresponds to the numerical measure of the possibility that a certain simple event Ei or composite event A occurs. It is represented by P(Ei) or P(A). There are three definitions for probability: Classical, Relative, and Subjective.

Whatever the definition, the probability must obey two properties:

1. The probability of a simple event Ei or a composite event A is positioned in the range between 0 and 1. That is: 0 ≤ P(Ei) ≤ 1 or 0 ≤ P(A) ≤ 1.

2. The sum of the probabilities of all single events Ei is equal to 1 .

Classical probability

Assume that two or more events have the same probability of occurrence such that they are considered equally possible.

• Simple event: P(Ei) = 1/n , 

where n is the number of simple events.

• Composite event:  p(A) = |A|/|S|, 

where   |A| is the cardinality of set A, and |S| is the cardinality of set S and is equal to n.

An example of application of the Classical Probability in the experiment of throwing a dice once to find an answer to the following questions:

1. Probability of toss five-value: P(E5) = 1/6 .

2. Probability of tossing an even-value: Given A = {2, 4, 6}, and S = {1, 2, 3, 4, 5, 6}, then P(A) = |A|/|S| = |{2,4,6}|/|{1,2,3,4,5,6}| = 3/6 = 1/2 = 0.5

Relative or Empirical probability

If an experiment is repeated n times, and an event E is observed f times, then, the probability of occurring event E will be P(E) = f/n, where: f is the frequency of event E, and n is the number of repetitions of the experiment.

An example of Relative Probability could be employed in the experiment of throwing a dice 1000 times, and the frequency of each face is given in the following table.