A definition is a statement of the meaning of a word, whereas a synonym is another word of the same meaning. A synonym may serve as a definition, if the meaning of the synonym is already known, while one is ignorant of the meaning of the word.

It would appear as if a valid definition of probability is ‘the likelihood of an event’. However, likelihood is as vague a term as probability. This can be seen if likelihood is defined as ‘the probability of an event’. Thus, to state that probability is the likelihood of an event, is not to define probability, but to identify likelihood as a synonym for probability.

In contrast, probability can be defined without the synonym of likelihood. Probability is the ratio of the favorable cases of an event to the total of all possible cases or outcomes of an event. What is wrong with this definition? It is based on human ignorance of facts and not upon facts themselves.

An application of this definition will show that it requires a veil of human ignorance. It is said that seven as the sum of two rolled ‘fair’ dice is a probability of one-sixth. However, this requires the human ignorance of the forces to which the dice are subjected in rolling them. The actual forces to which the dice are subjected determine exactly the outcome of the event and the sum evident in that outcome. Given these forces, the outcome will be a sum of seven or a sum of non-seven. The result has nothing to do with other cases or outcomes. Thus, the roll of a pair of dice is always a singular determinate case, having nothing in fact to do with (1) ‘favorable cases’ and (2) ‘all possible cases’. There are no other cases, except in the human imagination. To characterize the singular case as a probability is to place it within human imagination, or more accurately, to veil it in human ignorance.

Does this mean that there is no definition of probability, which is not conditioned by human ignorance? No, the unconditional definition of probability is purely mathematical. It is the ratio of a subset to a set. For example the set of all possible sums of two integers, each of which may be an integer from 1 through 6, is a set of 36 elements. The size of the subset of sevens among this set is 6. Thus the probability of the sum seven for this set is one-sixth. When we play games involving the roll of two dice we typically adopt the relationships of probability of the subsets of this set of 36 as a mutual convention.

It should be evident that when we treat the definition of probability as the ratio of the favorable cases of an event to the total of all possible cases or outcomes of an event, we are proposing an analogy, which is based on human ignorance.

The definitions of random and non-random are also relevant to the meaning of probability.