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1: Probability Systems

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    • 1.1: Likelihood
      This page outlines the significance of probability models across various fields and traces their historical development from gambling to formalization by key figures like Kolmogorov. It covers fundamental concepts such as trials, outcomes, and events, explaining how events can be represented using set theory. The page includes examples of events, definitions of mutually exclusive and impossible events, and introduces Boolean combinations and DeMorgan's rules.
    • 1.2: Probability Systems
      This page introduces probability measures in classical probability, defining sample spaces and events, and outlining properties like nonnegativity and countable additivity. It then expands to the Kolmogorov model, discussing additivity, subadditivity, and unions of events, emphasizing flexible modern probability models and their application to infinite outcomes.
    • 1.3: Interpretations
      This page explores the formal model of probability, highlighting its role in representing uncertainty and likelihood, with key properties such as non-negativity and the summation of mutually exclusive events. It distinguishes between objective and subjective interpretations of probability, discusses the odds of events, and introduces partitions. Events are defined as subsets of outcomes, emphasizing their properties and the formation of sigma algebras.
    • 1.4: Problems on Probability Systems
      This page covers exercises on sets, events, and probability, examining how to describe sets and their relationships. It includes examples of calculating outcomes, probability measures, and verifying conditions for valid measures, such as additivity. The content involves deriving a probability measure from a partition of events and positive constants, demonstrating its non-negativity, normalization, and additivity.

    This page titled 1: Probability Systems was last modified on Sun, 25 Oct 2026 20:34:12 GMT and is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Paul Pfeiffer via source content that was edited to the style and standards of the LibreTexts platform.