Development and Application of Probability Theory

The Development of Probability Theory
Name
Institution
The Development of Probability Theory
Introduction
According to Merriam Webster Online Dictionary (2018), probability is the ‘ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.’ Simply put, it is the chance that a given event will occur. Therefore, for probability, there must be several mathematical axioms which must be met to accurately predict the likelihood of a certain event. The first axiom is that the ‘probability of any event is a nonnegative real number.’ This means that there is no negative probability and the lowest chance is zero, and it cannot be infinite. Therefore, the probable set of numbers that an event can have are just real numbers. The second axiom of probability is that ‘the probability of the entire sample space is one.’ This means that anything with absolute certainty has a probability of 100% or one. The final axiom is that ‘the probability deals of mutually exclusive events are mutually exclusive.’ Therefore, the probability of the sum of more than one event is the sum of the probabilities. It may be easy to understand these axioms and guess that they were incepted when probability theory was incepted, however, the definition and reference of the theorem has evolved for centuries.
The first person who developed an interest in analyzing probability mathematically is Gerolamo Cardan who wrote a rudimentary manuscript that attempted to explain the probability of certain outcome when dice are rolled. Gambling prompted mathematicians, scientists, and players to explore an idea that could determine the chance of a future event stemming from the necessity to achieve a predictable balance between risks and the probable gain from them. Gamblers wanted to have developed a formula that gave them certainty in their participation such that they could increase their potential gain and protect themselves against potential losses. The people who are credited with the inception of the probability theory are Blaise Pascal (1623-1662) and Pierre de Fermat (1601-1665). The two were contemplating a mathematical problem posed by Chevalier de Mere in 1654 on probability. There is documented correspondence of Pascal and Fermat on the subject which laid the fundamental groundwork for the theory.
In what they called the problem of the dice (Berlinghoff & Gouvêa, 2004), the question posed by Chevalier sparked further inquiry in solving questions based on probable outcomes. From their correspondence, there are two interesting points that come up. Pascal decided to pursue the method which his Italian predecessors had given up on the problem of the points and declared there exists no determined solution that can be used to determine the division of stakes. Pascal gave a formula that asserted that if one player required n victories to win the stakes, then the other lacked m victories. Pascal developed the Pascal triangle using this concept to determine the probable winner for every game.
The second interesting point fronted by pascal enumerated all possible events once the game continued. He described a scenario...