What is Probability theory: Definition and 103 Discussions

Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.
Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes, which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion.
Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.

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    How Do You Calculate the Probability of Getting the Flu?

    Hello, I was hoping somebody can guide me with this problem, or perhaps help walk me through it. Its for a stats (probability theory) class. The question reads: -- Suppose that the probability of exposure to the flu virus during flu season is 0.3. People can get a flu vaccine which...
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    Probability Theory Q&A: Rolling 5 Dice to Find Probability of 2 Different Values

    Hello, I have two questions regarding probaility, i was hoping some body can help me out. I know that this is a "Physics Forum" However, i thought somebody might still beable to help :) When rolling 5 distinuishable dice, find the probability that there are two different values? I did...
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    Categories and Probability Theory

    Does anyone know if there is any study of probability theory from the point of view of category theory? I was trying to find some references but I just found something about probabilistic automatons and precategories. I would like to see something about probability distributions and categories...
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