Page 331 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Concept of Probability

We live in a world dominated by uncertainty. Change is the only permanent phenomenon. We can
never predict the nature and direction of change in our lives. Sometimes change is planned, but more
often, change is unplanned. Even in cases of planned change, it is not possible to avoid uncertainty.
There is a perceived need to be accurate (up to an extent) and prepared in this uncertain environment.
Our need to cope with this unavoidable uncertainty of life has led to the study of probability theory.
There might have been many occasions when we have said that the chances are 50-50 or there is a
70% chance of India winning the match, and so on. By making these statements, we try to attach
some probability of the event happening or not happening. If we look at the wider picture, all these
statements are related to the concept of probability. Therefore, there is a general understanding about
the concept of probability, but there is a problem in terms of its proper application-oriented
understanding.
In simple words, probability is the likelihood or chance that a particular event will or will not occur.
The theory of probability provides a quantitative measure of uncertainty or likelihood of occurrence
of different events resulting from a random experiment, in terms of quantitative measures ranging
from 0 to 1. This means that the probability of a certain event is 1 and the probability of an impossible
event is 0. In other words, a probability near 0 indicates that an event is unlikely to occur whereas a
probability near 1 indicates that an event is almost certain to occur. For example, suppose an event is
the success of a new product launched. A probability 0.90 indicates that the new product is likely to
be successful whereas a probability of 0.15 indicates that the product is unlikely to be successful in
the market. A probability of 0.50 indicates that the product is just as likely to be successful as not.

Probability is a concept that we all understand. In our daily life, we use words like chance,
possibility, likelihood, and of course, probability.

Some Basic Concepts
Before we give definition of the word probability, it is necessary to define the following basic concepts
and terms widely used in its study:
(1) An Experiment
When we conduct a trial to obtain some statistical information, it is called an experiment.
Examples: (i) Tossing of a fair coin is an experiment and it has two possible outcomes:
Head (H) or Tail (T).
(ii) Rolling a fair die is an experiment and it has six possible outcomes:
appearance of 1 or 2 or 3 or 4 or 5 or 6 on the upper most face of a die.
(iii) Drawing a card from a well shuffled pack of playing cards is an experiment
and it has 52 possible outcomes.
(2) Events
The possible outcomes of a trial/experiment are called events. Events are generally denoted by
capital letters A, B, C, etc.
Examples: (i) If a fair coin is tossed, the outcomes - head or tail are called events.
(ii) If a fair die is rolled, the outcomes 1 or 2 or 3 or 4 or 6 appearing up are
called events.
(3) Exhaustive Events
The total number of possible outcomes of a trial/experiment are called exhaustive events. In
other words, if all the possible outcomes of an experiment are taken into consideration, then
such events are called exhaustive events.

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