Page 265 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
n
experiment and in view of the fact that P S P e i 1 (from axiom II), we can assign a
i 1

1
probability equal to to every elementary event or, using symbols, we can write
n
1
P e
i for i = 1, 2, .... n.
n
Further, if there are m elementary events in an event A, we have,
e
in
i
1 1 1 m n A , . ., number of elements A
P A ...... m times
i
in
e
n n n n n S , . ., number of elements S
We note that the above expression is similar to the formula obtained under classical
definition.
2. Using Statistical Definition: Using this definition, the assignment of probabilities to
various elementary events of a sample space can be done by repeating an experiment a
large number of times or by using the past records.
3. Subjective Assignment: The assignment of probabilities on the basis of the statistical and
the classical definitions is objective. Contrary to this, it is also possible to have subjective
assignment of probabilities. Under the subjective assignment, the probabilities to various
elementary events are assigned on the basis of the expectations or the degree of belief of
the statistician. These probabilities, also known as personal probabilities, are very useful
in the analysis of various business and economic problems where it is neither possible to
repeat the experiment nor the outcomes are equally likely.
It is obvious from the above that the Modern Definition of probability is a general one
which includes the classical and the statistical definitions as its particular cases. Besides
this, it provides a set of mathematical rules that are useful for further mathematical
treatment of the subject of probability.

12.3.7 Theorems on Probability

Theorem 1:

P 0 , where is a null set.
Theorem 2:

P A 1 P A , where A is compliment of A.

Figure 12.2: Venn Diagram

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