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Introduction to Probability

Introduction to Probability. Onur DOĞAN. Introduction to Probability. The Classical Interpretation of Probability The Frequency Interpretation of Probability The Subjective Interpretation of Probability. Types of Experiments. Experiment and Event :

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Introduction to Probability

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  1. Introduction to Probability Onur DOĞAN

  2. Introduction to Probability • The Classical Interpretation of Probability • The Frequency Interpretation of Probability • The Subjective Interpretation of Probability

  3. Types of Experiments Experiment and Event: An experiment is anyprocess, real or hypothetical, in whichthe possible outcomes can be identified ahead of time. An event is a well-defined setof possible outcomes of the experiment.

  4. Sample Space The collection of all possible outcomes of an experiment is called thesample space of the experiment. A: Event S: Collection of all events

  5. The Empty Set Some events are impossible. For example, when a die is rolled, it • is impossible to obtain a negative number. Hence, the event that a negative number • will be obtained is defined by the subset of S that contains no outcomes.

  6. Operations of Set Theory

  7. Operations of Set Theory • Intersection and union operations have associativeand distributive properties . • De Morgan’s Law

  8. AxiomsandBasicTheorems • Axiom(1) / Axiom(2) / Axiom(3) • Further Properties of Probability:

  9. AdditionRule/MultipicationRule

  10. Permutations • Obtaining Different Numbers:

  11. Combinations

  12. Example

  13. BinomialCoefficients

  14. MultinomialCoefficients

  15. MultinomialCoefficients

  16. Example

  17. The Union of a Finite Number of Events

  18. TheUnion of ThreeEvents

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