Mathematics NCERT Grade 9, Chapter 15: Probability- We all feel that there are some probabilities that we face in our daily lives such as it will probably rain today, most probably she will go today, etc. Many interesting activities are given in the first part to catch the attention of students and to make the process of learning more exciting for them. These activities can be performed with the help of coins.
Different terms can be learned by performing these activities:
• Each toss of a coin is called a trial.
• Trial is an action which results in one or several outcomes
• Event for an experiment is the collection of some outcomes of the experiment
The very first section given after a short introduction is Probability- an Experimental Approach.
• An event for an experiment is the collection of some outcomes of the experiment
• The empirical probability P(E) of an event E is given by:
P(E) = (Number of trials in which E has happened)/ Total number of trials
• The probability of an event lies between 0 and 1. (0 and 1 inclusive)
• Probability of an impossible event is 0 and that of a sure event is 1.
This section is explained with 5 activities. Various solved examples are given to explain the topic. This chapter contains only 1 exercise i.e 15.1. It contains questions of different kinds. The data given for the probability is generally listed in tabular form.
For a quick revision key points of chapter are given in the end.

#### Question 1:

In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Number of times the batswoman hits a boundary = 6

Total number of balls played = 30

∴ Number of times that the batswoman does not hit a boundary = 30 − 6 = 24 ##### Video Solution for probability (Page: 283 , Q.No.: 1)

NCERT Solution for Class 9 math - probability 283 , Question 1

#### 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.

Total number of families = 475 + 814 + 211

= 1500

(i) Number of families having 2 girls = 475 (ii) Number of families having 1 girl = 814 (iii) Number of families having no girl = 211  Therefore, the sum of all these probabilities is 1.

##### Video Solution for probability (Page: 283 , Q.No.: 2)

NCERT Solution for Class 9 math - probability 283 , Question 2

#### 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.

Number of students born in the month of August = 6

Total number of students = 40  ##### Video Solution for probability (Page: 283 , Q.No.: 3)

NCERT Solution for Class 9 math - probability 283 , Question 3

#### 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.

Number of times 2 heads come up = 72

Total number of times the coins were tossed = 200 ##### Video Solution for probability (Page: 283 , Q.No.: 4)

NCERT Solution for Class 9 math - probability 283 , Question 4

#### Question 5:

An organization 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 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.

Number of total families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

(i) Number of families earning Rs 10000 ­− 13000 per month and owning exactly 2 vehicles = 29

Hence, required probability, (ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579

Hence, required probability, (iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10

Hence, required probability, (iv) Number of families earning Rs 13000 ­− 16000 per month and owning more than 2 vehicles = 25

Hence, required probability, (v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062

Hence, required probability, ##### Video Solution for probability (Page: 283 , Q.No.: 5)

NCERT Solution for Class 9 math - probability 283 , Question 5

#### 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:

 Marks Number of student 0 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − above 7 10 10 20 20 15 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.

Totalnumber of students = 90

(i) Number of students getting less than 20 % marks in the test = 7

Hence, required probability, (ii) Number of students obtaining marks 60 or above = 15 + 8 = 23

Hence, required probability, ##### Video Solution for probability (Page: 284 , Q.No.: 6)

NCERT Solution for Class 9 math - probability 284 , Question 6

#### 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 dislike 135 65

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it

Total number of students = 135 + 65 = 200

(i) Number of students liking statistics = 135 (ii) Number of students who do not like statistics = 65 ##### Video Solution for probability (Page: 284 , Q.No.: 7)

NCERT Solution for Class 9 math - probability 284 , Question 7

#### 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?

(i) Total number of engineers = 40

Number of engineers living less than 7 km from their place of work = 9

Hence, required probability that an engineer lives less than 7 km from her place of work, (ii) Number of engineers living more than or equal to 7 km from their place of work = 40 − 9 = 31

Hence, required probability that an engineer lives more than or equal to 7 km from her place of work, (iii) Number of engineers living within km from her place of work = 0

Hence, required probability that an engineer lives within km from her place of work, P = 0

##### Video Solution for probability (Page: 284 , Q.No.: 8)

NCERT Solution for Class 9 math - probability 284 , Question 8

#### Question 9:

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.

This is an activity based question. Students are advised to perform this activity by yourself.

##### Video Solution for probability (Page: 285 , Q.No.: 9)

NCERT Solution for Class 9 math - probability 285 , Question 9

#### Question 10:

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.

This is an activity based question. Students are advised to perform this activity by yourself.

##### Video Solution for probability (Page: 285 , Q.No.: 10)

NCERT Solution for Class 9 math - probability 285 , Question 10

#### 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.

Number of total bags = 11

Number of bags containing more than 5 kg of flour = 7

Hence, required probability, ##### Video Solution for probability (Page: 285 , Q.No.: 11)

NCERT Solution for Class 9 math - probability 285 , Question 11

#### Question 12:

 Concentration of SO2 (in ppm) Number of days (frequency ) 0.00 − 0.04 4 0.04 − 0.08 9 0.08 − 0.12 9 0.12 − 0.16 2 0.16 − 0.20 4 0.20 − 0.24 2 Total 30

The above frequency distribution table represents 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.

Number days for which the concentration of sulphur dioxide was in the interval of 0.12 − 0.16 = 2

Total number of days = 30

Hence, required probability, ##### Video Solution for probability (Page: 285 , Q.No.: 12)

NCERT Solution for Class 9 math - probability 285 , Question 12

#### Question 13:

 Blood group Number of students A 9 B 6 AB 3 O 12 Total 30

The above frequency distribution table represents 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.

Number of students having blood group AB = 3

Total number of students = 30

Hence, required probability, ##### Video Solution for probability (Page: 285 , Q.No.: 13)

NCERT Solution for Class 9 math - probability 285 , Question 13

View NCERT Solutions for all chapters of Class 9