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:
∵ 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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