Probability: Theory and Examples
Maria Catherine C. Borres (Contributor)
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Probability theory is a fundamental pillar of modern mathematics with relations to other mathematical areas like algebra, topology, analysis, geometry or dynamical systems. The principal objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Probability deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event." The probability of the occurrence of an event can be expressed as a fraction or a decimal from 0 to 1. Events that are unlikely will have a probability near 0, and events that are likely to happen have probabilities near 1. In any probability problem, it is very important to identify all the different outcomes that could occur. For instance, in the question about the dice, you must figure out all the different ways the dice could land, and all the different ways you could roll a seven. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics. Probability theory had its start in the 17th century, when two French mathematicians, Blaise Pascal and Pierre de Fermat carried on a correspondence discussing mathematical problems dealing with games of chance. Initially, probability theory mainly considered discrete events, and its methods were mainly combinatorial. Eventually, analytical considerations compelled the incorporation of continuous variables into the theory. Contemporary applications of probability theory run the gamut of human inquiry, and include aspects of computer programming, astrophysics, music, weather prediction, and medicine. This Text contains probability basics and rules, as well as the fundamental law of total probability and Bayes' theorem.
About the Author
Catherine Borres is currently taking up Master of Arts in Education Major in Mathematics in Philippine Normal University - Manila. She is currently working as a Content Developer for Mathematics at the Affordable Private Education Center (APEC Schools).
- Contributor: Maria Catherine C. Borres
- Imprint: Arcler Education Inc
- ISBN13: 9781680945874
- Number of Pages: 259
- Packaged Dimensions: 152x229mm
- Format: Hardback
- Publisher: Arcler Education Inc
- Release Date: 2016-11-30
- Binding: Hardback
- Biography: Catherine Borres is currently taking up Master of Arts in Education Major in Mathematics in Philippine Normal University - Manila. She is currently working as a Content Developer for Mathematics at the Affordable Private Education Center (APEC Schools).