Definition of Probability and Probability as an Enigma

• The general definition of probability lies in the idea of "likelihood." The interpretation as to what likelihood is, however, is not agreed upon. Nevertheless, all theories of probability agree that a probability is a real number in the range of 0 to 1. Yet this is where probabilists end their agreements. How you calculate a probability and how you can use a probability to make inferences depends on the theory being supported.
  
  

Objective Probability

• Objective probability theory states that a probability is an inherent trait of an object. For example, dice inherently have six sides, all flat and all consuming the same amount of space. Thus, because of this symmetry, the probability of a roll coming up a specific number is 1/6. The implication of this theory is that probabilities can be calculated by inspecting an object or knowing an event; experiments need not be run.
  
  

Relative Frequency

• This theory of probability states that probability, although an objective quantity, can never be known in the real world. The supporters of the relative frequency theory define the probability of an event as being the number of times that event occurs in respect to the number of times the event could have occurred, supposing that we observe such a situation infinitely many times. Of course, it is impossible to roll dice infinitely many times, thereby precluding a person from obtaining the true probability. In other words, those who agree with the relative frequency definition of probability will not agree that rolling a 4 has a 1/6 chance of occurring unless a large number of controlled experiments are run.
  
  

Subjective Probability

• Subjective probability is the opposite of objective probability, as it states quite boldly that probability is not real. Supporters of this theory state that the probability of an event only exists in an individual's mind. Thus, the same event can have multiple probabilities when being analyzed by many. To sum up this stance, probability is defined as a measure of belief that a certain event will happen. For example, an individual may choose to believe that the probability of rolling a "4" is actually 1/2.