Lecture 03 Probability

MGT 601: Statistical Inference

Lecture 03
Dr. MUMTAZ AHMED

Objectives of Current Lecture
In the current lecture:
 Introduction to Probability
 Definition and Basic concepts of probability
 Some basic questions related to probability
 Laws of probability
 Conditional probability

 Independent and Dependent Events
 Related Examples

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Probability
 Probability (or likelihood) is a measure or estimation of how likely it is that

something will happen or that a statement is true.
For example, it is very likely to rain today or I have a fair chance of passing annual examination or A will probably win a prize etc.
In each of these statements the natural state of likelihood is expressed.
 Probabilities are given a value between 0 (0% chance or will not happen) and 1

(100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
 Probability

is used widely in different fields such as: mathematics, statistics, economics, management, finance, operation research, sociology, psychology, astronomy, physics, engineering, gambling and artificial intelligence/machine learning to, for example, draw inferences about the expected frequency of events.

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Probability
Probability theory is best understood through the application of the modern set theory.
So first we are presenting some basic concepts, notations and operations of set theory that are relevant to probability.

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Sets
A set is a well-defined collection or list of distinct objects.
For example:
 A group of students
 Number of books in a library
 Integers between 1and 100
 The objects that are in a set are called members or elements of that set.
 Sets are usually denoted by capital letters such as A, B, C, Z etc, while their

elements are represented by small letters such as a, b, c and z etc.
 Elements are enclosed by braces to represent a set, e.g.