Page 335 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes From the above figure, it is clear that as the number of trials increases, the probability of head
tends to approach 0.5 and when the number of trials is infinite, i.e., n → ∞ , the probability of
getting head is equal to 0.5.
(3) Subjective Approach
According to this approach, probability to an event is assigned by an individual on the basis of
evidence available to him. Hence probability is interpreted as a measure of degree of belief or
confidence that a particular individual reposes in the occurrence of an event. But the main
problem here is that different persons may differ in their degree of confidence even when same
evidence is offered.
26.2 Uses of Theory of Probability

The theory of probability has its origin in the games of chance related to gambling such as tossing a
die, tossing a coin, drawing a card from a deck of 52 cards and drawing a ball of a particular colour
from a bag. But in modern times, it is widely used in the field of statistics, economics, commerce and
social sciences that involve making predictions in the face of uncertainty. The importance of probability
is clear from the following points:
(1) Probability is used in making economic decision in situations of risk and uncertainty by sales
managers, production managers, etc.
(2) Probability is used in theory of games which is further used in managerial decisions.
(3) Various sampling tests like Z-test, t-test and F-test are based on the theory of probability.
(4) Probability is the backbone of insurance companies because life tables are based on the theory
of probability.
Thus, probability is of immense utility in various fields.
Probability Scale

The probability of an event always lies between 0 and 1, i.e., ≤≤0 p 1 . If the event cannot take place,
i.e., impossible event, then its probability will be zero, i.e., P(E) = 0 and if the event is sure to occur,
then its probability will be one, i.e., P(E) = 1.
Calculation of Probability of an Event
The following steps are to be followed while calculating the probability of an event:
(1) Find the total number of equally likely cases, i.e., n
(2) Obtain the number of favourable cases to the event,. i.e., m
(3) Divide the number of favourable cases to the event (m) by the total number of equally likely
cases (n). This will give the probability of an event.
Symbolically,
Probability of occurrence of an event E is:
Numberof favourablecases to E m
P(E) = =
Totalnumberofequallylikelycases n
Similarly, Probability of non-occurrence of event E is:

P(E) = 1 – P(E)
The following examples will illustrate the procedure:
Example 1: Find the probability of getting a head in a tossing of a coin.
Solution: When a coin is tossed, there are two possible outcomes - Head or Tail.
Total number of equally likely cases = n = 2
Number of cases favourable to H = m = 1

330 LOVELY PROFESSIONAL UNIVERSITY