NCERT Solutions for Class 9th Maths Chapter 15
Probability
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Exercise 15.1
Question 1:
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 the boundary.
Solution: Consider the event of batswoman not hitting the ball as E. Here, the total number of trials is
30. The batswoman has hit 6 boundaries in her innings.
Therefore,
Number of times the boundary is not hit by her is,
30 – 6 = 24
Now,
[No. of balls she didn't hit to the boundary]P(E) =
[Total no. of balls played by her]
24 4P(E) =
30 5=
So, the required probability is 4
5.
Question 2:
1500 families with 2 children were selected randomly and the following
data were recorded:
Number of girl in a
family 2 1 0
Number of families 475 814 211
Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl
Also check whether the sum of these probabilities is 1.
Solution: (i)
Here, total number of the families = 1500
The number of families with 2 girls = 475,
Let the event of selecting the family with 2 girls be X, so,
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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No. of families with 2 girlsP(X) =
Total no. of families
475 19P(X) =
1500 60=
Hence, the probability of family having 2 girls is 19
60.
(ii)
The number of families having 1 girl are 814. Consider the event of selecting the family with
1 girl as Y, so,
No. of families with 1 girlP(Y) =
Total no. of families
814 407P(Y) =
1500 750=
Hence, the probability of family having 1 girl is 407
750.
(iii)
The number of families having no girl is 211. Consider the event of selecting a family with
no girl as a child be Z, so,
No. of families with no girlP(Z) =
Total no. of families
211P(Z) =
1500
Hence, the probability of family having no girls is 211
1500.
Question 3:
[Refer to Example 5, Section 14.4, and Chapter 14.]
Find the probability that a student of the class was born in August.
Solution: Refer to example 5,
40 students from a particular section of Class IX were asked about their birth months and the
following graph was prepared from the obtained data:
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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The total number of students = 40.
From the graph, the number of students born in August is 6.
P (student born in august 6 3
40 20=
Hence, the probability that the student born in august is 3
20.
Question 4:
Three coins are tossed simultaneously 200 times with the following
frequencies of different outcomes:
Outcome 3 heads 2 heads 1 heads No heads
Frequency 23 72 77 28
If the three coins are simultaneously tossed again, compute the probability
of 2 head coming up.
Solution: The total number of tosses = 200
Number of getting 2 heads = 72
The no. of times 2 heads have shown up.P(E) =
Total no. of trial
72 9P(E) =
200 25=
Hence, the probability of getting 2 heads is 9
25 .
Question 5:
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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An organization selected 2400 families at random and surveyed them to
determine a relationship between income level and the number of vehicles
in the family. The information gathered is listed in the table below:
Suppose a family is chosen. Find the probability that the family chosen is
(i) Earning Rs. 10000−13000 per month and owning exactly 2 vehicles.
(ii) Earning Rs. 16000 or more per month and owning exactly 1 vehicle.
(iii) Earning less than Rs. 7000 per month and does not own any vehicle.
(iv) Earning Rs. 13000−16000 per month and owning more than 2
vehicles.
(v) Owning not more than 1 vehicle.
Solution: Total number of families = 2400.
(i)
Number of families who has earning Rs. 10000 −13000 per month and owning exactly 2
vehicles is 29.
29Probability
2400=
Hence, the probability of families earning 10,000 – 13000 per month and owning exactly 2
vehicles is 29
2400.
(ii)
Number of families who has earning Rs. 16000 or more per month and owning exactly 1
vehicle = 579.
579 193Probability
2400 800= =
Hence, the probability of families earning Rs. 16000 or more per month and owning exactly 1
vehicle is 193
800.
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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(iii)
Number of families who has earning less than Rs. 7000 per month and does not own any
vehicle = 10.
10 1Probability
2400 240= =
Hence, the probability of families earning less than Rs. 7000 per month and does not own any
vehicle is 1
240.
(iv)
Number of families who has earning Rs. 13000−16000 per month and owning more than 2
vehicles = 25.
25 1Probability
2400 96= =
Hence, the probability of families earning Rs. 13000−16000 per month and owning more
than 2 vehicles is 1
96.
(v)
Number of families who has owning not more than 1 vehicle.
10 0 1 2 1 160 305 535 469 579 2062= + + + + + + + + + =
2062 1031Probability
2400 1200= =
Probability = 2062
2400=
1031
1200
Hence, the probability of families who has owning not more than 1vehicle is 1031
1200.
Question 6:
A teacher wanted to analyze the performance of two sections of students in
a mathematics test of 100 marks. Looking at their performances, she found
that a few students got under 20 marks and a few got 70 marks or above.
So she decided to group them into intervals of varying sizes as follows:
0−20, 20−30… 60−70, 70−100. Then she formed the following table: [Refer
to table 14.7, chapter 14.]
Marks Number of students 0 − 20
20 − 30
30 − 40
40 − 50
50 − 60
7
10
10
20
20
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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60 − 70
70 − above 15
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.
Solution: (i)
Total number of students = 90
The students who scored less than 20% in math’s = 7
Probability = 7
90
(ii)
The students who scored more than 60 or equal to 60 = 23,
Total number of students are 90.
Probability = 23
90
Question 7:
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.
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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Solution:
The total number of students are 200.
(i)
The students who like statistics = 135
Probability (students who like statistics)135 27
200 40= = .
(ii)
The students who dislike statistics = 65.
Probability (students who dislike statistics) 65 13
200 40= =
Question 8:
Refer to Q.2, Exercise 14.2.
The distance (in km) of 40 engineers from their residence to their place of
work were found as follows.
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
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
𝟐 km from her place of work?
Solution: (i)
Total number of engineers = 200
The total number of engineers who have their home in 7 km from work place = 9
Probability = Number of engineers living at a distance of less than 7 km form work place
Total number of engineers
= 9
40.
(ii)
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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The total number of engineer who have their home in more than or equal to 7 km from the
work place are 40 - 9 = 31
Probability = 31
40
(iii)
The number of engineers who live within 1
2 km of the work place is 0.
Probability = 0
40 = 0.
Question 9:
Activity: Note the frequency of two – wheeler, three-wheeler and four-
wheelers going past during a time – interval in front of school gate. Find
the probability that any one vehicle out of the total vehicles you have
observed is a two-wheeler.
Solution: The respective frequencies of different types of vehicles after observing in front of the school
gate in time interval 6:30 to 7:30 am are:
Types of vehicles
Frequency
Two-wheelers
Three-wheelers
Four-wheelers
550
250
80
Total number of vehicle,
( ) 550 250 80
880
n S = + +
=
Number of two-wheelers,
( ) 550n E =
Therefore, probability of observing two-wheelers is,
( )
( )550 5
880 8
n E
n s= =
Question 10:
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 him/her is divisible by 3? Remember that a number is divisible
by 3, if the sum of its digits is divisible by 3.
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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Solution: A three digit number start from 100 to 999.
Total number of three digit numbers = 999 - 99 = 900.
Multiple of 3 in three digit numbers = {102, 105, ....., 999}
Number of multiples of 3 in three digit number = 900
3 = 300
i.e., n(E) = 300
The probability that the number written by Her
Him is divisible by 3 =
n(E)
n(S) =
300
900 =
𝟏
𝟑.
Hence, the probability that the number written by her / him is divisible by 3 is 𝟏
𝟑.
Question 11: Eleven bags of wheat flour, each marked 5 kg, actually
contained the following weights of flour (in kg):
4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00
Find the probability that any of these bags chosen at random contains
more than 5 kg of flour.
Solution: The number of bags which contain more than 5 kg of wheat flour is 7.
We have total 11 bags, so the required probability of choosing the bag with more than 5 kg of
wheat flour is
No. of bags with more than 5 kg of flourP(E) =
Total number of bags of flour
7P(E) =
11
Hence, the probability that any of these bags chosen at random contains more than 5 kg of
flour is 7
11
Question 12:
A study was conducted to find out the concentration of Sulphur dioxide in
the air in parts per million (ppm) of a certain city. The frequency
distribution of the data obtained for 30 days is as follows:
Concentration of SO2 (in ppm) Number of days (frequency)
0.00 − 0.04 4
0.04 − 0.08 9
NCERT Solutions for Class 9th Maths Chapter 15
Probability
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0.08 − 0.12 9
0.12 − 0.16 2
0.16 − 0.20 4
0.20 − 0.24 2
Total 30
Solution:
The concentration of Sulphur dioxide in the interval 0.12 – 0.16 is on 2 days and the total
number of days is 30.
Probability (concentration of Sulphur dioxide in the interval 0.12 – 0.16) = 2
30=
1
15
Question 13:
The blood groups of 30 students of class VIII are given in the following
frequency distribution table:
Blood group Number of students
A 9
B 6
AB 3
O 12
TOTAL 30
Use this table to determine the probability that a student of this class,
selected at random, has blood group AB.
Solution:
The number of students who have the blood group AB = 3
Total number of students = 30
Required Probability = Number of students having blood group AB
Total number of students
The probability which we require is3
30=
1
10 .
Hence, the required probability is 1
10
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