Ancient Mathematics: Probability Theory During the Seventeenth Century

Ancient Mathematics: Probability Theory During the Seventeenth Century
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Ancient Mathematics: Probability Theory During the Seventeenth Century
Introduction
Participation in gaming and gambling is as old as humankind and the idea of probability is thought to be as old as humanity. However, the conception that it was possible to predict outcomes to some degree of accuracy was never conceivable until the 16th and the 17th centuries. The idea was prompted by the need to achieve a predictable balance between risks and gains to make profits from gambling. Statistics, a field closely related to probability began in the 1600s following John Grant's work on “Bills of Mortality” in 1662 (Burton, 1999). In this manual, Graunt illustrated the most common causes of death and age expectancy in London. Probability was initially inspired through gambling, and the original work on the theory was done by Girolamo Cardano (1501-1576), who specialized in physics and mathematics (Hald, 2003). Cardano in his manual “Liber de Ludo Aleae” discusses several basic constructs of probability theory complete with a systematic examination of gambling challenges. However, his work had no significant impact on the growth of the theory since it never featured in print format until 1663, which made it receive little attention. Later years saw Chevalier de Mere's invention of a gambling system in 1654, which made him convinced that it would help in making money. De Mere decided to bet an amount that he could roll a twelfth in 24 rolls of the two dice. As de Mere started losing his money, he requested Blaise Pascal to investigate his gambling approach (Grinstead & Snell, 1997). Pascal could later discover that de Mere’s system was vulnerable to losing almost 51% each time it is applied. Pascal could, later on, become intrigued with probability and started studying more probabilistic challenges, which he shared with Pierre de Fermat, another famous mathematician and they established the foundation of probability theory (Dale 1999). This paper explores the advancement of probability theory and illustrates how the theory emerged from the need to solve fundamental challenges in predicting outcomes and gambling for profits.
The theory of probability is largely concerned with establishing the connection between the frequency of event occurrence (Grinstead & Snell, 1997). For instance, in flipping a coin, it will be curious to know the times the heads will show up if that coin was to be flipped a hundred times. Answering this problem requires both empirical and theoretical approaches and the example of flipping a coin illustrates the differences that manifest in the two ways of solving probability problems. While using the theoretical approach, it can be reasoned that in each flip, there are only two chances, that of a tail and ahead. By assuming that each of the two events is likely to be equal, then the probability that the heads will appear is only 0.5 or half.
On the other hand, the empirical approach avoids such assumptions of having equal likelihoods. By performing a real flipping experiment, it is possible to count the number of tails and heads each time the coin is tossed. In this case, the probability of the heads appearing is the actual count of heads divided by the total flips made. The two branches of mathematics, probability, and statistics are mainly concerned with laws that govern random events, which include data gathering, analysis, interpretation, and presentation. The theory of probability has its origin in the study of insurance and gambling in the 17th century and is today an invaluable tool of natural and social sciences. Initial developments in probability theory are first recorded in 1550 in Cardano’s work whose manuscript addressed the chances of outcomes when a dice is rolled (Grinstead & Snell, 1997). In his work, Cardano presented a basic description of probability, but his manual was lost. Had Cardano’s manual not been misplaced, he would be named as the founder of probability theory. Unfortunately, his manual was only discovered and discovered in 1663 leaving room for other independent discoveries.
Today’s mathematics of chance dates to a collaboration between Pierre de Fermat and Blaise Pascal and their motivation emanated from a challenge about gambling or game of probability that was remarkably suggested by Chevalier de Mere, a philosophical gambler. Legend has it that the theory of probability started as a mathematical branch with correspondence with Pascal and Pierre de Fermat in 1654 (Burton, 1999). However, historical records indicate that years before Fermat and Pascal mathematicians still tackled problems of probability in nature. For instance, the estimation of economic wealth and populations dates back to antiquity. Examples include Emperor Augustus' use of balance sheets, the counting of Israelites, and the counting of inventory of possessions of William the Conqueror (Burton 1999). It would be more appropriate to mention that Pascal and Fermat offered important links in developing the theory of probability as known today. De Mere had questioned on the accurate stake divisions when gambling or game of probability can be interrupted. In a typical problem, when two players, say player X and player Y are gambling in a game of three points, each with a wager of 32 pistoles and is stoped after player X has two points with player Y having one, the theory of probability should solve how much each should receive.
Developing from the above problem, Pascal and Fermat provided dissimilar solutions even after settling on the same numerical answer. Each of the mathematicians defined a set of symmetrical or equal cases and solutions to the problem to answer the problem through making a comparison of the winnings for player X and player Y. However, Fermat described his solution in the form of probabilities or occurrences by reasoning that two additional games would occur in any of the cases to define wins. He reasoned that four possible changes were possible in the fair game of occurrence. According to Fermat, player X has a chance of winning twice (XX) or player X might win first before player Y. equally, player Y might win first before player X or YY. Of the four chances, only the last chance would lead to a victory for b and therefore, the odds for player X should be 3:1. This implies that there are distributions of 47 ...