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Sachin Kaushal, Lovely Professional University Unit 7: Modern Approach to Probability

Unit 7: Modern Approach to Probability Notes

CONTENTS

Objectives
Introduction
7.1 Axiomatic or Modern Approach to Probability
7.1.1 Definition of Probability (Modern Approach)

7.2 Theorems on Probability
7.3 Theorems on Probability
7.4 Summary of Formulae
7.5 Keywords

7.6 Self Assessment
7.7 Review Questions
7.8 Further Readings

Objectives

After studying this unit, you will be able to:
 Explain Axiomatic or Modern Approach to Probability
 Describe Theorems on Probability

 Discuss Theorems on Probability (Contd.)
Introduction

In last unit, you have studied about probability. A phenomenon or an experiment which can
result into more than one possible outcome, is called a random phenomenon or random
experiment or statistical experiment. Although, we may be aware of all the possible outcomes
of a random experiment, it is not possible to predetermine the outcome associated with a
particular experimentation or trial.
Consider, for example, the toss of a coin. The result of a toss can be a head or a tail, therefore, it
is a random experiment. Here we know that either a head or a tail would occur as a result of the
toss, however, it is not possible to predetermine the outcome. With the use of probability
theory, it is possible to assign a quantitative measure, to express the extent of uncertainty,
associated with the occurrence of each possible outcome of a random experiment.

7.1 Axiomatic or Modern Approach to Probability

This approach was introduced by the Russian mathematician, A. Kolmogorov in 1930s. In his
book, 'Foundations of Probability' published in 1933, he introduced probability as a function of
the outcomes of an experiment, under certain restrictions. These restrictions are known as
Postulates or Axioms of probability theory. Before discussing the above approach to probability,
we shall explain certain concepts that are necessary for its understanding.

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