Probability: classical, frequency-based and subjective approaches

Probability can be defined as a tool to manage uncertainty. Whenever an event is neither the certain one (with probability=1) nor the impossible one (probability=0), we are facing an uncertain situation, hence we need to attribute our event a likelihood of occurrence, which is, indeed, probability.

In this article, I’m going to present the three approaches to probability, which provide different interpretations of that concept and different assumptions to start with. Those approaches are:

• Classical approach
• Frequency-based (or empirical) approach
• Subjective approach

Let’s dwell on all of them.

Classical approach

This approach traces back to the field where probability was first sistematically employed, which is gambling (flipping coins, tossing dice and so forth). Gambling problems are characterized by random experiments which have n possible outcomes, equally likely to occur. It means that none of them is more or less likely to occur than other ones, hence they are said to be in a symmetrical position.

The idea of the classical approach is that, given a collection of k elements out of n (where 0≤k≤n), the probability of occurrence of the event…