Probability Meaning and Theorems

1. ECONOMIC STATISTICS
Dr. A. SATHEESH BABU
Assistant Professor, Department of Economics
VIVEKANANDA COLLEGE
(Residential & Autonomous –A Gurukula Institute of Life Training)
TIRUVEDAKAM WEST, MADURAI DIST– 625 234, TAMIL NADU

3. PROBABILITY
• Meaning
• In ordinary language, the word probable means
likely or chance.
• The word probability is used to denote the
happenings of a certain event, and the likelihood
of the occurrence of that event, based on past
experiences.
• Definition
• According to Morris Hamburg, A time series is a
set of observations arranged in chronological
order.
• According to Cecil H. Meyers, A time series may
defined as a sequence or repeated measurements
of a variable made periodically through time.

4. • Usefulness of Probability
• The theory of probability is based on
the Law of Statistical Regularity and
the Law of Inertia of Large Numbers.
• It is useful to derive different tests of
significance – Z tests, χ2 tests, etc.,
• It gives solution to betting and games
• It is a base for the decision theory
• It is very helpful to foresee the
uncertainties of betting and chances of
success.

5. • Terms used in Probability
• Random Experiment or Trial: An action or
an operation which can produce any result
or outcome is called a random experiment
or trial.
• Event: Any possible outcome of a random
experiment is called an event.
• Sample Space: A set or aggregate of all
possible outcomes is known as sample
space.
• Mutually Exclusive Events or Cases: The
occurrence of one event prevents the
occurrence of other event.
• Equally likely event: Two or more events
are said to be equally likely if the chance
of their happening is equal.

6. • Terms used in Probability
• Exhaustive Events: The total number of
possible outcomes of a random experiment
is called exhaustive events.
• Independent Events: The occurrence of
any one does not, in any way, affect the
occurrence of any other in the set.
• Dependent Events: The occurrence or non-
occurrence of one event in any trial
affects the probability of the other
subsequent trials.
• Simple and Compound Events: When a
single event take place, the probability of
its happening or not happening is known
as simple event.
• When two or more events take place
simultaneously, their occurrence is known
as compound event.

7. • Terms used in Probability
• Complementary Events: The
complement of an event A, means non-
occurrence of A and is denoted by Ā.
• Favourable Cases: The number of
outcomes which result in the happening
of a desired event are called favourable
cases.

8. Measurement of Probability
It is the oldest method of measuring
probability and it has origin from
gambling games.
According to this approach, the probability
is the ratio of favourable events to the
total number of equally likely events.
P =
Classical Approach (Priori Probability)
Total number of equally likely cases
Number of favourable cases

9. Measurement of Probability
The happening of an event is determined
on the basis of past experiences or on
the basis of relative frequency of
success in the past.
The relative frequency can be termed as a
measure of probability and it is
calculated on the basis of empirical or
statistical findings.
P (A) = lim
Relative Frequency Approach
(Posterior Probability)
n
m

10. Theorems of Probability
According to the Addition Theorem, if
two events are mutually exclusive, then
the probability of the occurrence of
either A or B is the sum of probabilities
of A and B.
P (A or B) = P (A) + P (B)
P (A or B) = P (A) + P (B) – P (A and B)
1. Addition Theorem
A) When Events are Mutually Exclusive
B) When Events are Not Mutually Exclusive

11. Theorems of Probability
According to the Multiplication Theorem,
if two events are independent, then the
probability that both will occur is equal
to the product of the respective
probabilities.
P (A and B) = P (A) x P (B)
2. Multiplication Theorem
A) When Events are Independent

12. Theorems of Probability
According to the Multiplication Theorem,
if two events are dependent, then the
probability is conditional. Two events A
and B are dependent, B occurs only when
A is known to have occurred.
P = P =
2. Multiplication Theorem
A) When Events are Dependent
A
B
P (A)
P (AB)
B
A
P (B)
P (AB)

13. Theorems of Probability
 This theorem is associated with the
name of Rev. Thomas Bayes.
 It is also known as inverse probability.
 The Baye’s theorem may by referred as,
the applications of the conditional
probability theory involves estimating
unknown probabilities and making
decisions on the basis of new sample
information.
3. Baye’s Theorem