Page 267 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 2. Multiplicative Theorem for Independent Events: If A and B are independent, the probability
of their simultaneous occurrence is given by


.
P A B P A P B .
Example: Two unbiased dice are tossed. Let w denote the number on the first die and r
denote the number on the second die. Let A be the event that w + r 4 and B be the event that
w + r 3 . Are A and B independent?

Solution:
The sample space of this experiment consists of 36 elements, i.e., n(S) = 36. Also, A = {(1, 1), (1, 2),
(1, 3), (2, 1), (2, 2), (3, 1)} and B = {(1, 1), (1, 2), (2, 1)}.
From the above, we can write

6 1 3 1
P A , P B
36 6 36 12
3 1
Also A  B {(1,1),(1,2),(2,1)} P A  B
36 12
Since P A  B P A P B , A and B are not independent.

Attributes
Notes
An attribute is a qualitative characteristics. One can only feel the presence or absence of
this characteristic while observing individuals or items under consideration. For example,
honesty, marriage, colour, beauty, etc., are attributes. It is, however, possible to classify
various individuals or items into two or more categories according to an attribute.

Self Assessment

Multiple Choice Questions:

12. .................................... techniques are often helpful in the enumeration of total number of
outcomes of a random experiment and the number of cases favourable to the occurrence of
an event.
(a) Counting (b) Discounting

(c) Estimation (d) Investigation
13. If the first operation can be performed in any one of the m ways and then a second
operation can be performed in any one of the n ways, then both can be performed together
in any one of the .......................... ways.

(a) m+n (b) m-n
(c) m × n (d) none

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