**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

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

Thus, the required probability =

Let the event of not hitting the boundary be represented by E, then

Thus, the required probability =

**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.

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

Solution:

Here, total number of families = 1500

**(i) ****∵**** Number of
families having 2 girls = 475
**

**∴**

**Probability of selecting a family having 2 girls =**

**(ii) ****∵**** Number of
families having 1 girl = 814
**

**∴**

**Probability of selecting a family having 1 girl =**

**(iii) Number of families having no girl = 211
Probability of selecting a family having no girl =
**

**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.

Find the probability that a student of the class was born in August.

Solution:

From the graph, we have

Total number of students bom in various months = 40

Number of students bom in August = 6

Solution:

From the graph, we have

Total number of students bom in various months = 40

Number of students bom in August = 6

**∴**

**Probability of a student of the Class-IX who was bom in August**

**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.

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

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 =**

**∴**

**Thus, the required probability =**

**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.

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)

Solution:

Here, total number of families = 2400

(i)

**∵**

**Number of families earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles = 29**

**∴**

**Probability of a family earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles =**

**(ii) ****∵**** Number of
families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
**

**∴**

**Probability of a family earning Rs. 16000 or more per month and owning exactly 1 vehicle =**

**(iii) ****∵**** Number of
families earning less than Rs. 7000 per month and do not own any vehicle = 10
**

**∴**

**Probability of a family earning less than Rs. 7000 per month and does not own any vehicle =**
=

**(iv) ****∵**** Number of
families earning Rs. 13000 – Rs. 16000 per month and owning more than 2
vehicles = 25
**

**∴**

**Probability of a family earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles =**
=

**(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 =**
=

**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.

(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 =

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 =

**(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 23 marks 60 or above =**

**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.

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)

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 =**
=

**(ii) ****∵**** Number of
students who do not like statistics = 65
**

**∴**

**Probability of selecting a student who does not like statistics =**
=

**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
**

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

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:

Here, total number of engineers = 40

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 is living less than 7 km from her place of work =**

**(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 is living at distance more than or equal to 7 km from her place of work =**

**(iii) ****∵**** The number
of engineers living within
**

**∴**

**Probability of an engineer who is living within**
km from her place of work =
= 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:

A class room activity for students.

**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

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 =**

**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 =**
=

**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, total number of students = 30

Solution:

Here, total number of students = 30

**∵**

**Number of students having blood group AB = 3**

**∴**

**Probability of a student whose blood group is AB =**
=
.

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