**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.

**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.

(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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