NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1

# NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1

## NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1

NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Chapter 15 Probability Ex 15.1.

Ex 15.1 Class 9 Maths 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 a boundary.

Solution:
Here, the total number of trials = 30
Number of times, the ball touched the boundary = 6
Number of times, the ball missed the boundary = 30 – 6 = 24
Let the event of not hitting the boundary be represented by E, then
P(E) = [No. of times the batswoman did not hit the boundary]/ [Total number of balls she played] = 24/30 = 4/5
Thus, the required probability = 4/5

Ex 15.1 Class 9 Maths Question 2.
1500 families with 2 children were selected randomly, and the following data were recorded:

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:
Here, total number of families = 1500

(i) Number of families having 2 girls = 475
Probability of selecting a family having 2 girls = 475/1500=19/60

(ii) Number of families having 1 girl = 814
Probability of selecting a family having 1 girl = 814/1500 = 407/750

(iii) Number of families having no girl = 211
Probability of selecting a family having no girl = 211/1500
Now, the sum of the obtained probabilities
= 19/60 + 407/750 + 211/1500 = (475 + 814 + 211)/1500 = 1500/1500 = 1
i.e., Sum of the above probabilities is 1.

Ex 15.1 Class 9 Maths Question 3.
In a particular section of class IX, 40 students were asked about the month 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:
From the graph, we have
Total number of students born in various months = 40
Number of students born in August = 6
Probability of a student of the Class IX who was born in August = 6/40 = 3/20

Ex 15.1 Class 9 Maths Question 4.
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

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

Solution:
Total number of times the three coins are tossed = 200
Number of outcomes in which 2 heads coming up = 72
Probability of 2 heads coming up = 72/200 = 9/25
Thus, the required probability = 9/25

Ex 15.1 Class 9 Maths 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.

Suppose a family is chosen. Find the probability that the family chosen is:
(i) earning ₹ 10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹ 7000 per month and does not own any vehicle.
(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Solution:
Here, total number of families = 2400
(i)
Number of families earning ₹ 10000 – ₹ 13000 per month and owning exactly 2 vehicles = 29
Probability of a family earning ₹ 10000 – ₹ 13000 per month and owning exactly 2 vehicles = 29/2400

(ii) Number of families earning 16000 or more per month and owning exactly 1 vehicle = 579
Probability of a family earning 16000 or more per month and owning exactly 1 vehicle = 579/2400

(iii) Number of families earning less than 7000 per month and do not own any vehicle = 10
Probability of a family earning less than 7000 per month and does not own any vehicle = 10/2400 = 1/240

(iv) Number of families earning 13000 – 16000 per month and owning more than 2 vehicles = 25
Probability of a family earning 13000 – 16000 per month and owning more than 2 vehicles = 25/2400 = 1/96

(v) Number of families owning not more than 1 vehicle
= [Number of families having no vehicle] + [Number of families having only 1 vehicle]
= [10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579] = 14 + 2048 = 2062
Probability of a family owning not more than 1 vehicle = 2062/2400 = 1031/1200

Ex 15.1 Class 9 Maths Question 6.
A teacher wanted to analyse 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:

(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:
Total number of students = 90
(i) From the given table, number of students who obtained less than 20% marks = 7
Probability of a student obtaining less than 20% marks = 7/90

(ii) From the given table, number of students who obtained marks 60 or above = [Number of students in class-interval 60 – 70] + [Number of students in the class interval 70 – above]
= 15 + 8 = 23
Probability of a student who obtained marks 60 or above = 23/90

Ex 15.1 Class 9 Maths 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:

Find the probability that a student chosen at random
(i) likes statistics,
(ii) does not like it.

Solution:
Total number of students whose opinion is obtained = 200
(i)
Number of students who like statistics = 135
Probability of selecting a student who likes statistics = 135/200 = 27/40

(ii) Number of students who do not like statistics = 65
Probability of selecting a student who does not like statistics = 65/200 = 13/40

Ex 15.1 Class 9 Maths 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 ½ km from her place of work?

Solution:
Here, total number of engineers = 40

(i) Number of engineers who are living less than 7 km from their work place = 9
Probability of an engineer who lives less than 7 km from her place of work = 9/40

(ii) Number of engineers living at a distance more than or equal to 7 km from their work place = 31
Probability of an engineer who lives at a distance more than or equal to 7 km from her place of work = 31/40

(iii) The number of engineers living within ½ km from their work place = 0
Probability of an engineer who lives within ½ km from her place of work = 0/40 = 0

Ex 15.1 Class 9 Maths 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:
It is an activity. Students can do it themselves.

Ex 15.1 Class 9 Maths 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 digit is divisible by 3.

Solution:
It is an activity. Students can do it themselves.

Ex 15.1 Class 9 Maths 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:
Here, total number of bags = 11
Number of bags having more than 5 kg of flour = 7
Probability of a bag having more than 5 kg of flour = 7/11

Ex 15.1 Class 9 Maths 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:

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:
Here, total number of days = 30
The number of days on which the sulphur dioxide concentration is in the interval 0.12 – 0.16 = 2
Probability of a day on which sulphur dioxide is in the interval 0.12 – 0.16 = 2/30 = 1/15

Ex 15.1 Class 9 Maths Question 13.
The blood groups of 30 students of class VIII are recorded as follows:
A, B, 0, 0, AB, 0, A, 0, B, A, 0, B, A, 0, 0, A, AB, 0, A, A, 0, 0, AB, B, A, B, 0
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 random, has blood group AB.

Solution:

Here, the total number of students = 30
Number of students having blood group AB = 3
Probability of a student whose blood group is AB = 3/30 = 1/10.

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