NCERT Solutions for Class 9 Maths Chapter 15 Probability

NCERT Solutions for Class 9 Maths Chapter 15 Probability Statistics are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 15 Probability.

Board	CBSE
Textbook	NCERT
Class	Class 9
Subject	Maths
Chapter	Chapter 15
Chapter Name	Probability
Exercise	Ex 15.1
Number of Questions Solved	13
Category	NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 15 Probability

 Chapter 15 Probability Ex 15.1

Question 1.
In a cricket match, a bats woman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
Solution:
Given, a bats woman play 30 balls, therefore total number of trials = 30 and number of events of hitting the boundary = 6
Now, number of balls in which she is not hitting the boundary
= 30 – 6 = 24
∴ The probability that she did not hit a boundary = =

Question 2.
1500 families with 2 children were selected randomly, and the following data were recorded :

Number of girls 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:
Let E₀, E₁ and E₂ be the event of getting no girl, 1 girl and 2 girls.

Question 3.
In a particular section of class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained.

Find the probability that a student of the class was born in August.
Solution:
Total number of students in class IX, n(S) = 40
Number of students born in the month of August, n(E) = 6
Probability, that the students of the class was born in August
=  =  = 

Question 4.
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	77	28

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Solution:
In tossing of three coins, getting two heads comes out 72 times. i.e.,   n(E) = 72
The total number of tossed three coins n(s) = 200
∴ Probability of 2 heads coming up =  =  = 

Question 5.
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 :
Solution:

Montly income(in Rs)	Vehicles per Family
Less Than 7000	0 10	1 160	2 25	Above 2 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 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 selected by the organisation, n(S) = 2400
(i) The number of families earning Rs. 10000 – 13000 per month and owning exactly 2 vehicles,
n(E₁) = 29

Question 6.
Table

Marks	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.
Solution:
(i) Total number of students in a class, n(S) = 90
The number of students less than 20% lies in the interval 0 – 20,
i.e., n(E) = 7
∴ The probability, that a student obtained less than 20% in the Mathematics
test =  =

(ii) The number of students obtained marks 60 or above lies in the marks interval 60 – 70 and 70-above
i.e., n(F) =15+8 = 23
∴  The probability that a student obtained marks 60 or above = = 

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	135
Dislike	65

Find the probability that a student chosen at random
(i) likes statistics
(ii) does not like it.
Solution:
Total number of students, n(S) = 200
(i) The number of students who like Statistics n(E) = 135
∴ The probability, that the student like Statistics
=  =

(ii) The number of student Who does not like Statistics, n (E) = 65
∴ The probability, that the student does not like Statistics =  =  =

Question 8.
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 km from her place of work?
Solution:
Total number of engineers lives, n(S) = 40
(i) The number of engineers whose residence is less than 7 km from their place, n(E) = 9
∴ The probability that an engineer lives less than 7 km from their place of work
=  = 

(ii) The number of engineers whose residence is more than or equal to 7 km from their place of work, n(F) = 40 – 9 = 31
∴ The probability, that an engineer lives more than or equal to 7 km from their place of work
=  = 

(iii) The number of engineers whose residence within km from their place of work, i.e., n(G) = 0
∴ The probability, that an engineer lives within km from their place
=  =  =0

Question 9.
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?
Solution:
After observing in front of the school gate in time interval 6 : 30 to 7 : 30 am respective frequencies of different types of vehicles are :

Types of Vehicles	Frequency
Two wheelers	550
Three wheelers	250
Four wheelers	80

∴  Total number of vehicle, n(S) = 550 + 250 + 80 = 880
Number of two-wheelers, n(E) = 550
robability of observing two-wheelers =  =  = 

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 her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.
Solution:
Suppose, there are 40 students in a class.
∴ The probability of selecting any of the student = = 1
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 =  = 300
i.e.,  n(E) = 300
∴  The probability that the number written by her/him is divisible by 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 total number of wheat flour bags, n(S) = 11
Bags, which contains more than 5 kg of flour, (E)
= {5.05, 5.08, 5.03, 5.06, 5.08, 5.04, 5.07,}
∴ n(E)=7
∴  Required probability =  = 

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 data obtained for 30 days is as follows :

0.03	0.08	0.08	0.09	0.04	0.17
0.16	0.05	0.02	0.06	0.18	0.20
0.11	0.08	0.12	0.13	0.22	0.07
0.08	0.01	0.10	0.06	0.09	0.18 .
0.11	0.07	0.05	0.07	0.01	0.04

You were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days
Solution:
Now, we prepare a frequency distribution table

Interval	Frequency
0.01-0.04	5
0.04-0.08	11
0.08-0.12	7
0.12-0.16	2
0.16-0.20	4
0.20-0.24	1
Total	30

The total number of days for data, to prepare sulphur dioxide, n(S) = 30
The frequency of the sulphur dioxide in the interval 0.12-0.16, n(E) = 2
∴ Required probability =  =  = 

Question 13.
The blood groups of 30 students of class VIII are recorded as follows:
A,B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB,
B,A, O, B, A, B, O
You were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at randon, has blood group AB.

Blood group	Frequency
A	9
B	6
O	12
AB	3
Total	30

The total number of students in class VIII, n(S) = 30
The number of students who have blood group AB, n(E) = 3
∴ The probability that a student has a blood group
AB =  = 

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