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3: Counting and Probability

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    182260

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    • 3.1: The Multiplication Rule for Counting
      This section explains the Multiplication Rule for Counting, a method for calculating probabilities and combinations through examples like cupcake counting and creating IDs. It generalizes this approach for various scenarios, including password and license plate combinations with specific repetition rules. The text also presents exercises for practice and problem-solving in different contexts, such as making meals and belts, emphasizing the utility of multiplication in simplifying counting tasks.
    • 3.2: Permutations and Combination
      This section covers permutations, focusing on their calculation through the Multiplication Rule for Counting and factorials. It provides various examples, including Olympic swimming heats and roles for students, to illustrate applications and the importance of order in permutations. The text explains permutations of identical items and includes exercises for practice. Additionally, it mentions that the page contains questions from MyOpenMath, which is under a Creative Commons license.
    • 3.3: Fundamental Concepts of Probability
      This section covers learning objectives about probability, including experiments, outcomes, sample spaces, and events, illustrated with Monopoly. It discusses tree diagrams for complex outcomes, theoretical vs. empirical probabilities using examples like dice and spinners, and the historical contributions of Gerolamo Cardano to gambling strategies.
    • 3.4: The Addition and Complement Rule for Probability
      This section explains key probability concepts, including complementary and mutually exclusive events, and the Addition Rule for calculating "or" probabilities while avoiding double counting. It provides various examples using cards and dice, along with practical applications involving survey data and two-way tables. Additionally, it includes enrollment data from a liberal arts college, accompanied by related probability questions about student selection based on class year or major.
    • 3.5: Odd and Expected Value
      This section discusses expected value in the context of random games like roulette, dice, and card games, explaining how to calculate and interpret it through examples. It highlights the negative expected value often faced by players in gambling scenarios. Additionally, it covers expected values in life insurance and raffles, emphasizing their financial implications. Historical figures Blaise Pascal and Pierre de Fermat are referenced for their contributions.

    Thumbnail: Two standard gaming dice. (CC BY-SA 3.0 Unported; Steaphan Greene via Wikipedia)

    This page titled 3: Counting and Probability is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.