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When Aristotle expressed the mind-boggling aphorism “Probable impossibilities are to be preferred to improbable possibilities,” he might not be aware that this sentence would confuse the whole universe with one of the most perplexing subjects that have ever been created: Probability Theory. What was Probability about that makes a lot of fuss in the minds of laymen but much less to mathematicians particularly to a Fermat’s or Pascal’s?
Probability Theory is the branch of mathematics concerned with analysis of random. (Boggled?) Probability Theory is a division of mathematics that deals with measuring or establishing quantitatively the possibility that an occurrence or experiment will have a particular outcome. (Still confusing?) Probability defines the chance of something or event happening. (It comes clearer now.)
Students of Probability Theory, with minds free from worries and problems can hack it more easily. They know in school that habitual use of the theory comes from repeated experiments of the interpretation of probability. Probability is used to provide the amount of beliefs based on opinions and feelings rather than of facts. It is the inner sense of a gambler that he could win in a game of betting.
Students taking up the course should have in mind that the content of Probability Theory is naturally mathematical. To understand it fully, the chief instrument to use is a genuine grasp of Calculus: differentiation and integration. The course familiarizes the students with the idea of chance. To make them cope with the doubt, provide their needs with any kind of subject – economics, signal processing, engineering or scientific course – where uncertainty happens. By showing examples and illustrations, general principle and problems are explained.
Mathematical background comprising calculus and linear algebra serve as a condition to the study of probability theory. Learning the aspect of the theory prepares the students to the courses that include applied statistics, stochastic processes, mathematical finance, and actuarial science. Students should also learn the formulation of probability samples that describe the fundamental production of development and progression.
Probability with applications is introduced that include: basic probability samples, random variables, discrete and continuous probability distributions, calculation mathematical expectation and variance, independence, and simulations about probability. As the course concludes, every student should (1) have the full comprehension about probability theory regarding its principle or idea as an abstract material; and its methodology or system and approaches in the areas of practical, statistical, and experimental; (2) makes comparison with, or calculate its importance or value, and carry out the process of replication through the use of another; (3) the student should be able to employ the Minitab program in evaluating “probability distributions” (such as when the presumption of current for both negative and positive are evenly distributed, the body or material could be electrified); use Minitab in investigating data and encapsulating the result after conducting the review.
Let’s take a look at a demonstration on probability theory. When we toss a coin, we are experimenting. In the experiment, one or more possibilities would come out: heads and tails. (Of course, it would not stand on its circumferential edge.) This is true with the rolling of the die: there would be six possible results. The products of the experiments would be the probability theory.
Probability theory is not as early as the many parts of mathematics. In the 16th and 17th centuries, it sprouts through the investigations made by Cardano, Fermat and Pascal. Thanks to these famous mathematicians and philosophers that our mind were boggled up once more.