14. PROBABILITY

14. PROBABILITY

  • 14

    Probability

    This section introduces the fundamental concepts of probability, discussing theoretical and experimental approaches, including the definitions of favorable outcomes and the importance of equally likely outcomes.

  • 14.1

    Probability — A Theoretical Approach

    This section introduces the concept of theoretical probability, focusing on equally likely outcomes and key definitions.

  • 14.2

    Summary

    This section outlines key definitions and concepts related to theoretical probability.

    • Key Summary

    The chapter introduces the concept of probability, focusing on theoretical probability and empirical probability. It explains the importance of equally likely outcomes and provides various examples to illustrate how to calculate the probability of different events, including impossible and certain events. The chapter culminates in exercises that test the understanding of probability through real-world scenarios.

    Key Takeaways

    • The theoretical probability of an event E is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, assuming equally likely outcomes.
    • The probability of a sure event is 1, while the probability of an impossible event is 0, indicating that a favorable outcome is never achieved.
    • Elementary events consist of only one outcome, and the sum of the probabilities of all elementary events equals 1. For any event E, the probability of not E can be calculated using complementary probabilities.

    Key Concepts

    • Theoretical Probability: Defined as P(E) = Number of favorable outcomes / Total number of possible outcomes, used when outcomes are equally likely.
    • Empirical Probability: Based on observed outcomes and the frequency of the event occurring during trials, used when the theoretical approach is not feasible.
    • Elementary Event: An event that consists of a single outcome in an experiment.
    • Complementary Events: Two events are complementary if the occurrence of one means the other cannot occur, leading to P(E) + P(not E) = 1.