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Introduction to Probability Concepts

May 24, 2025

Lecture Notes on Probability

Introduction to Probability

  • Definition: Probability is a measure of the likelihood that an event will occur.
  • Applications: Used in various fields such as statistics, finance, gambling, science, and engineering.

Key Concepts

Basic Terms

  • Experiment: A process that leads to the occurrence of one and only one of several possible observations.
  • Outcome: A possible result of an experiment.
  • Event: A specific outcome or a set of outcomes of a random experiment.

Probability Principles

  • Sample Space (S): The set of all possible outcomes of an experiment.
  • Event (E): A subset of the sample space.
  • Probability of an Event (P(E)): Number of favorable outcomes divided by the total number of possible outcomes.
    • Formula: ( P(E) = \frac{n(E)}{n(S)} )

Types of Probability

  • Classical Probability: Based on the assumption that outcomes of an experiment are equally likely.
  • Empirical Probability: Based on observations and experiments.
  • Subjective Probability: Based on intuition or personal judgment.

Important Properties

  • The probability of any event is a number between 0 and 1.
  • The sum of probabilities of all mutually exclusive outcomes of an experiment is 1.
  • The probability of the complement of an event is 1 minus the probability of the event.
    • Formula: ( P(E') = 1 - P(E) )

Conclusion

  • Understanding probability is essential for making predictions about random events.
  • Probability forms the foundation of statistics and is critical in various decision-making processes.