Probability theory is a fundamental branch of mathematics that deals with the analysis of random phenomena. It provides a framework for predicting outcomes based on the likelihood of different events. In this tutorial, we will explore the basics of probability theory and its applications.
Key Concepts
- Random Experiment: A process that can result in more than one outcome.
- Sample Space: The set of all possible outcomes of a random experiment.
- Event: A subset of the sample space.
- Probability: A measure of the likelihood that an event will occur.
Basic Probability Rules
- Addition Rule: The probability of the union of two events is equal to the sum of their probabilities minus the probability of their intersection.
- Multiplication Rule: The probability of the intersection of two independent events is equal to the product of their probabilities.
- Complementary Rule: The probability of an event is equal to 1 minus the probability of its complement.
Applications
Probability theory has numerous applications in various fields such as finance, engineering, and statistics. For example, it is used to assess the risk of financial investments, predict the behavior of physical systems, and analyze data.
Further Reading
For a more in-depth understanding of probability theory, we recommend checking out our Advanced Probability Theory Tutorial.
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