Page 333 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Example: If two coins are tossed simultaneously and we shall be finding the probability of
getting two heads, then we are dealing with compound events.
(8) Independent Events
Two events are said to be independent if the occurence of one does not affect and is not affected
by the occurence of the other.
Examples: (i) In tossing a die twice, the event of getting 4 in the 2nd throw is independent
of getting 5 in the first throw.
(ii) In tossing a coin twice, the event of getting a head in the 2nd throw is
independent of getting head in the 1st throw.
(9) Dependent Events
Two events are said to be dependent when the occurence of one does affect the probability of
the occurence of the other events.
Examples: (i) If a card is drawn from a pack of 52 playing cards and is not replaced, this
will affect the probability of the second card being drawn.

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(ii) The probability of drawing a king from a pack of 52 cards is or . But
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if the card drawn (king) is not replaced in the pack, the probability of drawing
3
again a king is .
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Definition of Probability

The probability is defined in the following three different ways:
(1) Classical or Mathematical Definition
(2) Empirical or Relative Frequency Definition
(3) Subjective Approach.
(1) Classical or Mathematical Definition
This is the oldest and simplest definition of probability. This definition is based on the assumption
that the outcomes or results of an experiment are equally likely and mutually exclusive.
According to Laplace, “Probability is the ratio of the favourable cases to the total number of
equally likely cases”. From this definition, it is clear that in order to calculate the probability of
an event, we have to find the number of favourable cases and it is to be divided by the total
number of cases. For example, if a bag contains 6 green and 4 red balls, then the probability of
getting a green ball will be 6/4 + 6 = 6/10 because the total number of balls are 10 and the
number of green balls is 6.
Symbolically,

NumberofFavourableCases m
P(A) = p = =
TotalNumberofEquallyLikelyCases n
Where, P(A) = Probability of occurrence of an event A
m = Number of favourable cases
n = Total number of equally likely cases
Similarly,

m
P(A) = q = 1 – P(A) = −1
n
Where, P(A) = q = Probability of non-occurrence of an event A.

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