The Theory of Probability by Blaise Pascal - Research Paper Example

? The Importance and Application of Theory of Probability The Theory of Probability by Blaise Pascal served humanity for centuries until the present. It cannot be denied how the quantitative measure of chance can assist people in decision-making in various aspects of life. The analysis of the gambling laid foundation to more complicated logic and mathematical probability. Technology, morality, social science and physics all rely on probability. The Importance and Application of Theory of Probability Introduction Mathematics has helped people in quantifying things as the numerals offer the convenience of calculating objects. Throughout history, various theories and principles had been laid down by mathematicians to further strengthen and deepen the study of numbers, space and computations. Numbers have been the characters used in math while letters are usually used in language. The operations and proofs that are done throughout the development in the field of mathematics give way to the modernization and advancement of the human mind. One of the theories that led to the advancement is the Theory of Probability. The Theory of Probability comes from the word probable and the adjective probably. “Probably” is usually used in casual conversation like: Caesar probably visited Britain. The outbreak of a nuclear war is less probable now than it was 10 or 15 years ago. The likely winner is Miss Florida. The expanding universe theory is probably true. The door is probably locked. (Weatherford, 1982, p. 2) The word probably cannot describe probability in a specific way as adjectives are descriptive words. Once probably is said, it describes an object qualitatively. Probably pertains to qualitative description of frequency. Most people do not use probable in a mathematical sense as that word can also mean “possible, conceivable, plausible, reasonable and typical,” (Gigerenzer, 2007, p. 95). To define probability in an easy way, it pertains to the possibility of an event to occur. Putting the possibility in a mathematical perspective, it deals with the quantitative measure of the chance that an event will happen. Quantitative techniques are used to measure the uncertainty in a scientific manner and afterwards make quantitative conclusions with the help of logic (Bean, 2000, p. 1). In addition, uncertainty is concerned with the unknown or the insufficient information regarding the present and the future. The degree of uncertainty is linked with risk. Risk is the uncertain result which can be positive or negative. The positive risk is called opportunity while the negative risk is threat (Cretu, Stewart and Berrends, 2011, p. 4). Probability allows people to have calculated assessment of the unknown outcome. The theory can be elaborated in three ways as discussed in the succeeding paragraph. The Theory of Probability can be discussed using a classical method, simple property method and statistical method. Using classical method, the theory provides a standard measure for determining the uncertainties in the occurring events. Classical method can also be called mathematical method as an equation can be used to represent the theory: P (A) = n/N = No. of outcomes favorable to A/No. of outcomes in ? = v (A)/v (?) Where A = the event or subset of interested outcomes n = the number of outcomes ? = the set of all outcomes v (?) = the number of sample points in ? v (A) = the number of points in A (Bhat, 1999, p. 2) Another way of elaborating the Theory of Probability is through the use of simple property method. Additive property of addition is the basic form of probability theory. The following can illustrate the property: P (A?B) = P (A + B) = (m + n)/N = (m/N) = P (A) + P (B) […] Probability function possesses the following properties: (i) P(A) ? 0, (non-negativity); (ii) P(A1 + … + An) = ?n1 P(Ai), (Additivity), (iii) P(?) = 1 (normed) It follows immediately that P (?) = P (A + Ac) = P (A) + P (Ac) = 1, P (Ac) = 1 – P (A) ? 0, and hence 0 ? P (A) ? 1. Since P (?) = 1, P (?c) = p (?) = 0. If A ? B, B = A + B?Ac, and P (B) = P (A) + P (B?Ac) ? P (A). (Bhat, 1999, p. 3) The last method to describe the Theory of Probability is through statistical method. A sample situation would help illustrate the statistical method of probability like the chance of a new-born baby to be a boy. The method to get the probability is by checking the birth records at certain places and based on the proportion of baby boys in the past (Bhat, 1999, p. 4). Probability would greatly be needed in various fields of endeavors as it assists people in managing risks and uncertainty. The next part of the study would be focused on the importance and application of The Theory of Probability made by Blaise Pascal. Discussion People tend to avoid threats in their lives that show how people need the help of probability in decision-making in several aspects of life. Safety and success would be achieved when people can identify the success rate or learn the tendency of an event to occur quantitatively. In other words, various significant phenomena rely on the chance that they would occur as affected by several factors (Gnedenko and Khinchin, 1962, p. 119). In pursuit to measure the factors, statistics becomes a great discipline that assist people in managing risks. Probability became the fundamental concept of statistics. The Theory of Probability is also important in physical and biological sciences as both sciences are affected by the concept of chance. Nowadays probability also becomes useful in business and social sciences as stochastic models are created by psychologists to identify and improve learning while the game theory is used in economics to study market competition. In business, the expected quantity and random variables would all be important in the security issue based on the specific instructions of investor. For business managers, their planning would greatly be helped by probability as they decide facing uncertainty (Goldberg, 1960, v). In addition, specific situations in businesses also require the probability such as the success of a new product going to enter the market. Before the entrepreneur can go on with the new product, he must gather data on the factors that will affect the chance of success of the new product. The probability would be the guideline for the decision of the entrepreneur whether to pursue the goal or not. The next situation would be the role of the sales manager of a business firm that the firm must have monthly sales quota. The goal would depend upon initial data gathered on the factors and the success rate of increasing sales quota in certain places. With probability, investing would also be affected as sales forecast can be drawn from present data and when the probability is high, the investors can put more money to that business venture while an average sales probability would lead to less money invested (Beri, 2010, p. 180). In actuality, the probability became a classical established concept when Blaise Pascal became interested with gambling. The odds of winning in gambling games were computed as the chance of getting the prize. The classical probability then gave birth to modern and more complicated probability application (Bello, Britton and Kaul, 2010, p. 703). Pascal was concerned with the backgammon as the chance or the odds of a number to appear when the dice is thrown. The finding and creation of probability did not just concern the dicing and the gambling as the situation gave opportunity to Pascal to study the situations and devise techniques in knowing possible alternative outcomes. The practice in using probability is essential for practical decision-making whether the decision is for personal life or for business life (Kyburg and Teng, 2001, p. 10). Probability can also be used in moral sciences since the chances or risks are measured. Morals deals with the rightness or wrongness of action and the errors in actions can be measured by having more observations and learned through repetition. A testimony can also be measured by probability as errors in words can cause alteration of the truth (Laplace, 1995, p. 62). In relation to the morality and controversial issues, probability can also be applied in situation wherein death sentence is affected by the race of the victim and the defendant (Howell, 2010, p. 144). The probability can also be applied to complex machines such as a nuclear reactor as the machine needs to be handled with care. It would be dangerous once malfunction happens, so the probability that it would lead to accident can be used for preventive strategies. Markov Chains and Information Theory also depends on probability as transmission and conversion of the symbols to understandable messages would happen by chance. Smallpox also relied on probability as the spread of the disease and the resistance of people to the disease would be measured by probability (Tabak, 2004, pp. 101-108). Conclusion People truly need probability in everyday lives as using quantitative measures to identify and analyze the chances of certain events to occur can be vital in decision-making process. Making decisions is an essential part of life as the direction and purpose of life may come true with proper steps and actions based on projected possibilities. Modernization becomes possible and the advancement of technology and knowledge happen as people become more aware of the possibilities as continuous improvements in mathematics happen as the Theory of Probability serving as the basic foundation. The efforts of Blaise Pascal paid off as humanity owed it to him that started from just an analysis in gambling about the odds of winning through dicing. As the basic or classical probability changed as time passed by, the process becomes more complicated but can greatly reduce the errors and the chances of negative consequences to occur. References Bean, M. (2000). Probability: The science of uncertainty with applications to investments, insurance and engineering. USA: American Mathematical Society. Bello, I., Britton, J. and Kaul, A. (2010). Topics in contemporary mathematics, enhanced edition. USA: Cengage Learning. Beri, G. (2010). Business statistics 3rd ed. India: Tata McGraw Hill Education Pvt. Ltd. Bhat, B. (1999). Modern probability theory. India; New Age Publishers. Cretu, O., Stewart, R., and Berends, T. (2011). Risk management for design and construction. USA: John Wiley and Sons. Gigerenzer, G. (2007). Gut feelings: The intelligence of the unconscious. USA: Viking Penguin. Gnedenko, B. and Khinchin, A. (1962). An elementary introduction to the theory of probability. USA: Dover Publications. Goldberg, S. Probability: An introduction. USA: Dover Publications. Howell, D. (2010). Fundamental statistics for the behavioral sciences. USA: Cengage. Kyburg, H. and Teng, C. (2001). Uncertain inference. USA: Cambridge University Press. Laplace, P. (1995). A philosophical essay on probabilities. (A. I. Dale, Trans.). USA: Springer. (Orignial work published 1825). Tabak, J. (2004). Probability and statistics: the science of uncertainty. US: Facts On File Inc. Weatherford, R. (1982). Philosophical foundations of probability theory. London: Routledge and Kegan Paul Ltd. Read More