Definition of Probability

We will discuss here about the definition of probability, terms
related to probability, experiment, random experiment and trial.

Introduction

We often hear sentences like “it will possibly rain today”, “most
probably the train will be late”, “most likely Robert will not come today”,
etc.

In saying such sentences we try to measure the uncertainty
of an event (incidence).

In the study of probability, we try to measure numerically the
chances that favor the occurrence of an event.

The theory of probability originated from gambling. But at present this theory is so developed that it is being used in many fields of knowledge like economics, industry, engineering, navigation and defence. Some of the mathematicians who made considerable contribution to the development of the theory of probability are Blaise Pascal (1623 – 1662), Pierre de Fermat (1601 – 1665), Jacques Bernoulli (1654 – 1705), Abraham de Moivre (1667 – 1754), Simeon Dennis Poisson (1781 – 1840), Pafnuty Chebyshev (1821 – 1894), Andrei Markov (1856 – 1922) and Andrei Kolmogorov (1903 – 1987).

Terms Related to Probability:

Experiment: An action or process that results in well-defined
outcomes is known as an experiment.

Example: The toss of a coin is an experiment because it
results in a “head” or “tail”. So, the outcomes are well-defined.

Random Experiment:

If an experiment, although conducted
under identical conditions, can result in two or more known outcomes, it is
called a random experiment.

Trial:

The process of conducting an experiment is called a
trial which results in any one of the possible outcomes.

Definition of Probability:

The concept of probability
started in a statistical form of collecting data and it was called Empirical
Probability. Later a theoretical approach was introduced for probability and it
was called Theoretical Probability or Classical Probability.