INTRODUCTION TO PROBABILITY Onur DOAN 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: An experiment is any process, real or hypothetical, in which the possible outcomes can be identified ahead of time. An event is a well-defined set of possible outcomes of the experiment.

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

� � � 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.

Operations of Set Theory

Operations of Set Theory � Intersection and union operations have associative and distributive properties. � De Morgan’s Law

Axioms and Basic Theorems � � Axiom(1) / Axiom(2) / Axiom(3) Further Properties of Probability:

Addition Rule/Multipication Rule

Permutations � Obtaining Different Numbers:

Combinations

Example

Binomial Coefficients

Multinomial Coefficients

Multinomial Coefficients

Example

The Union of a Finite Number of Events

The Union of Three Events