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4: Independence of Events

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    • 4.1: Independence of Events
      This page covers the concept of independence in probability, explaining how it simplifies probability calculations by asserting that one event's occurrence does not affect another. It outlines key definitions, the product rule for determining independence, and differentiates between independence and mutual exclusivity.
    • 4.2: MATLAB and Independent Classes
      This page explores the use of MATLAB functions for calculating minterm probabilities of independent events and system reliability in different configurations. It emphasizes the independence in Boolean combinations, supported by examples and computational tools, while detailing methods for determining probabilities of combined events through m-functions.
    • 4.3: Composite Trials
      This page explores composite trials in probability, detailing component trials' sequential or simultaneous execution. It introduces Boolean algebra for expressing these events and presents Bernoulli trials. Additionally, it covers the binomial distribution related to Bernoulli trials, focusing on calculating the probability of obtaining \(k\) successes in \(n\) trials using formulas and MATLAB functions for efficiency.
    • 4.4: Problems on Independence of Events
      This page covers a range of exercises on probability, focusing on minterm probabilities, independence, and reliability analysis of systems. Key topics include calculating probabilities for independent events in various scenarios, such as dice rolls, games, and system configurations. It discusses the implications of event independence, methods for assessing relationships between events, and the use of binomial formulas.

    This page titled 4: Independence of Events 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.