UNIVERSITY OF MYSORE
TYPES OF PROBABILITY
UNIVERSITY OF MYSORE
of various terms
Approaches or types of probability
Theorems of probability
Discursion of problems
Probability theory is a very fascinating subject which
can be studied at various mathematical levels. Probability
is the foundation of statistical theory and applications.
Several mathematicians like Pascal, James Bernoulli,
De-Moivre, Bayes applied the theory of permutations and
combinations to quantify or calculate probability. Today
the probability theory has become one of the fundamental
technique in the development of Statistics.
The term “probability” in Statistics refers to the
chances of occurrence of an event among a large number of
If an experiment or trial is repeated under the same
conditions for any number of times and it is possible to
count the total number of outcomes is called as “Random
The set of all possible outcomes of a random
experiment is known as “Sample Space” and denoted by
set S. [this is similar to Universal set in Set Theory] The
outcomes of the random experiment are called sample
points or outcomes.
An ‘event’ is an outcome of a trial meeting a
specified set of conditions other words, event is
a subset of the sample space S.
Events are usually denoted by capital letters.
There are different types of events.
Null or impossible event is an event which
contains no outcomes.
Elementary event is an event which contains
only one outcomes.
Composite event is an event which contains
two or more outcomes.
Sure or certain event is an event which
contains all the outcomes of a sample space.
• Exhaustive Events:
The total number of all possible elementary outcomes
in a random experiment is known as ‘exhaustive events’. In
other words, a set is said to be exhaustive, when no other
The elementary outcomes which entail or favour the
happening of an event is known as ‘favourable events’ i.e.,
the outcomes which help in the occurrence of that event.
• Mutually Exclusive Events:
Events are said to be ‘mutually exclusive’ if the
occurrence of an event totally prevents occurrence of all
other events in a trial. In other words, two events A and B
cannot occur simultaneously.
• Equally likely or Equi-probable Events:
Outcomes are said to be ‘equally likely’ if there is no reason
to expect one outcome to occur in preference to another. i.e.,
among all exhaustive outcomes, each of them has equal chance
• Complementary Events:
Let E denote occurrence of event. The complement of E
denotes the non occurrence of event E. Complement of E is
denoted by ‘Ē’.
• Independent Events:
Two or more events are said to be ‘independent’, in a
series of a trials if the outcome of one event is does not affect the
outcome of the other event or vise versa.
In other words, several events are said to be
‘dependents’ if the occurrence of an event is affected by the
occurrence of any number of remaining events, in a series of
Measurement of Probability:
There are three approaches to construct a
measure of probability of occurrence of an event.
Frequency Approach and
Classical or Mathematical
In this approach we assume that an experiment or
trial results in any one of many possible outcomes, each
outcome being Equi-probable or equally-likely.
Definition: If a trial results in ‘n’ exhaustive, mutually
exclusive, equally likely and independent outcomes, and if
‘m’ of them are favourable for the happening of the event
E, then the probability ‘P’ of occurrence of the event ‘E’ is
Number of outcomes favourable to event E
Exhaustive number of outcomes
Empirical or Statistical
This approach is also called the ‘frequency’ approach
to probability. Here the probability is obtained by actually
performing the experiment large number of times. As the
number of trials n increases, we get more accurate result.
Definition: Consider a random experiment which is
repeated large number of times under essentially
homogeneous and identical conditions. If ‘n’ denotes the
number of trials and ‘m’ denotes the number of times an
event A has occurred, then, probability of event A is the
limiting value of the relative frequency m .
This approach was proposed by Russian
Mathematician A.N.Kolmogorov in1933.
‘Axioms’ are statements which are reasonably true and
are accepted as such, without seeking any proof.
Definition: Let S be the sample space associated with a
random experiment. Let A be any event in S. then P(A) is
the probability of occurrence of A if the following axioms
P(A)>0, where A is any event.
P(AUB) = P(A) + P(B), when event A and B are
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What are the problems faced
by HR people while using the
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sometimes they face the problems
like system slowdown or higher
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particular limitation in module than
work suffers, some HR people are
not comfortable in using system
efficiently so time is to be given in
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HRIS system is helping out in all the functions
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HRIS - Development
CONCIEVE & PLAN
HRIS - Implementation
Complete Business Solutions (CBS)
Build Your Own Integrated System
Multiple Systems and Data Hub Approach
HRIS – Example
Oracle/PeopleSoft HRMS (ver.
Automates the entire recruit-to-retire process.
A single integrated application includes the
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Compensation and benefits
Time management and real time
HRIS - Benefits
Higher Speed of retrieval and processing of data.
Reduction in duplication of efforts leading to reduced cost.
Ease in classifying and reclassifying data.
Better analysis leading to more effective decision making.
Higher accuracy of information/report generated.
Fast response to answer queries.
Improved quality of reports.
Better work culture.
Establishing of streamlined and systematic procedure.
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Employee – Self Management
HRIS - Disadvantages
It can be expensive in terms of finance and
It can be threatening and inconvenient.
Thorough understanding of what constitutes
quality information for the user.
Computer cannot substitute human beings.
“We are becoming
the servants in
thought, as in
action, of the
created them to
Management Information Systems: New
Approaches to Organization and Technology –
Upper Saddle River
Integrated HR Systems – Linda Stroh
III B. Com.