NCERT Solutions for Class 9 Clat Chapter 17 Introduction To Mathematical Modelling

Introduction To Mathematical Modelling Here is the CBSE Clat Chapter 17 for Class 9 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 9 Clat Introduction To Mathematical Modelling Chapter 17 NCERT Solutions for Class 9 Clat Introduction To Mathematical Modelling Chapter 17 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 9 Clat.

Question 1

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In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Solution

Let E be the event of hitting the boundary.

Then,
$straight P left parenthesis straight E right parenthesis equals fraction numerator his space the space boundary over denominator Total end fraction equals 6 over 30 equals 1 half equals 0.2$

∴ Probability of not hitting the boundary
= 1 – Probability of hitting the boundary
= 1 – P(E) = 1 – 0.2 = 0.8.

Question 5

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An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Monthly income

Vehicles per family

(in र)

0

1

2

Above 2

Less than 7000

10

160

25

0

7000-10000

0

305

27

2

10000-13000

1

535

29

1

13000–16000

2

469

59

25

16000 or more

1

579

82

88

Suppose a family is chosen. Find the probability that the family chosen is
(i) earning र 10000–13000 per month and owning exactly 2 vehicles.
(ii) earning र 16000 or more per month and owning exactly l vehicle.
(iii) earning less than र 7000 per month and does not own any vehicle.
(iv) earning र 13000–16000 per month and owning more than 2 vehicles.
(v) owning not more than I vehicle.

Average

View solution

Sponsor Area

Number of girls in a family	2	1	0
Number of families	475	814	211

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	71	28

Marks (out of 100)	Number of students
0-20	7
20-30	10
30-40	10
40-50	20
50-60	20
60-70	15
70–above	8
Total	90

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NCERT Solutions for Class 9 Clat Chapter 17 Introduction To Mathematical Modelling

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

In a particular section of Class IX, 40 students were asked about the months of their birth, the following graph was prepared for the data so obtained. Find the probability that a student of the class was bom in August.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome

3 heads

2 heads

1 head

No head

Frequency

23

72

71

28

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Marks (out of 100)

Number of students

0-20

7

20-30

10

30-40

10

40-50

20

50-60

20

60-70

15

70–above

8

Total

90

(i) Find the probability that a student obtained less than 20% in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.

Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within $1 half$ km from her place of work?

Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3 ? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

Monthly income	Vehicles per family
(in र)	0	1	2	Above 2
Less than 7000	10	160	25	0
7000-10000	0	305	27	2
10000-13000	1	535	29	1
13000–16000	2	469	59	25
16000 or more	1	579	82	88

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NCERT Solutions for Class 9 Clat Chapter 17 Introduction To Mathematical Modelling

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

In a particular section of Class IX, 40 students were asked about the months of their birth, the following graph was prepared for the data so obtained. Find the probability that a student of the class was bom in August.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No head Frequency 23 72 71 28 If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Marks (out of 100) Number of students 0-20 7 20-30 10 30-40 10 40-50 20 50-60 20 60-70 15 70–above 8 Total 90 (i) Find the probability that a student obtained less than 20% in the mathematics test.(ii) Find the probability that a student obtained marks 60 or above.

To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table: Opinion Number of students like dislike 135 65 Find the probability that a student chosen at random(i) likes statistics,(ii) does not like it.

Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within km from her place of work?

Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3 ? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome

3 heads

2 heads

1 head

No head

Frequency

23

72

71

28

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Marks (out of 100)

Number of students

0-20

7

20-30

10

30-40

10

40-50

20

50-60

20

60-70

15

70–above

8

Total

90

(i) Find the probability that a student obtained less than 20% in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.

Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within $1 half$ km from her place of work?