NCERT Textbook Chapter 15 - Probability, Mathematics, Class 9 Class 9 Notes | EduRev

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Class 9 : NCERT Textbook Chapter 15 - Probability, Mathematics, Class 9 Class 9 Notes | EduRev

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PROBABILLITY 271
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65
CHAPTER 15
PROBABILITY
It is remarkable that a science, which began with the consideration of
games of chance, should be elevated to the rank of the most important
subject of human knowledge. —Pierre Simon Laplace
15.1 Introduction
In everyday life, we come across statements such as
(1) It will probably rain today.
(2) I doubt that he will pass the test.
(3) Most probably, Kavita will stand first in the annual examination.
(4) Chances are high that the prices of diesel will go up.
(5) There is a 50-50 chance of India winning a toss in today’s match.
The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the
statements above involve an element of uncertainty. For example, in (1), ‘probably
rain’ will mean it may rain or may not rain today. We are predicting rain today based
on our past experience when it rained under similar conditions. Similar predictions are
also made in other cases listed in (2) to (5).
The uncertainty of ‘probably’ etc can be measured numerically by means of
‘probability’ in many cases.
Though probability started with gambling, it has been used extensively in the fields
of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather
Forecasting, etc.
Page 2


PROBABILLITY 271
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65
CHAPTER 15
PROBABILITY
It is remarkable that a science, which began with the consideration of
games of chance, should be elevated to the rank of the most important
subject of human knowledge. —Pierre Simon Laplace
15.1 Introduction
In everyday life, we come across statements such as
(1) It will probably rain today.
(2) I doubt that he will pass the test.
(3) Most probably, Kavita will stand first in the annual examination.
(4) Chances are high that the prices of diesel will go up.
(5) There is a 50-50 chance of India winning a toss in today’s match.
The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the
statements above involve an element of uncertainty. For example, in (1), ‘probably
rain’ will mean it may rain or may not rain today. We are predicting rain today based
on our past experience when it rained under similar conditions. Similar predictions are
also made in other cases listed in (2) to (5).
The uncertainty of ‘probably’ etc can be measured numerically by means of
‘probability’ in many cases.
Though probability started with gambling, it has been used extensively in the fields
of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather
Forecasting, etc.
272 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-15\Chap-15 (02-01-2006).PM65
15.2 Probability – an Experimental Approach
The concept of probability developed in a very
strange manner. In 1654, a gambler Chevalier
de Mere, approached the well-known 17th
century French philosopher and mathematician
Blaise Pascal regarding certain dice problems.
Pascal became interested in these problems,
studied them and discussed them with another
French mathematician, Pierre de Fermat. Both
Pascal and Fermat solved the problems
independently. This work was the beginning
of Probability Theory.
The first book on the subject was written by the Italian mathematician, J.Cardan
(1501–1576). The title of the book was ‘Book on Games of Chance’ (Liber de Ludo
Aleae), published in 1663. Notable contributions were also made by mathematicians
J. Bernoulli (1654–1705), P . Laplace (1749–1827), A.A. Markov (1856–1922) and A.N.
Kolmogorov (born 1903).
In earlier classes, you have had a glimpse of probability when you performed
experiments like tossing of coins, throwing of dice, etc., and observed their outcomes.
You will now learn to measure the chance of occurrence of a particular outcome in an
experiment.
Activity 1 : (i) Take any coin, toss it ten times and note down the number of times a
head and a tail come up. Record your observations in the form of the following table
Table 15.1
Number of times Number of times Number of times
the coin is tossed head comes up tail comes up
10 — —
Write down the values of the following fractions:
Number of times a head comes up
Total number of times the coin is tossed
and
Number of times a tail comes up
Total number of times the coin is tossed
Blaise Pascal
(1623–1662)
Fig. 15.1
Pierre de Fermat
(1601–1665)
Fig. 15.2
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