# NCERT Solutions for Class 9 Maths Chapter 15 Probability

Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 9 Maths Chapter 15 Probability Exercise 15.1

Q1 ) 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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Number of times the batswoman hits a boundary = 6

Total number of balls played = 30

Thus, Number of times that the batwoman does not hit a boundary
= 30 - 6
= 24

So, we get that,

$$P = \frac{Number of times when she does not hit boundary}{Total number of balls played}$$
$$P = \frac{24}{30} = \frac{4}{5}$$

Therefore, the probability that she did not hit a boundary is $$\frac{4}{5}$$.

Q2 ) 1500 families with 2 children were selected randomly, and the following data were recorded:

 No. of girls in a family No. of families 2 1 0 475 814 211

Compute the probability of a family,chosen at random, having
i) 2 girls
ii) 1 girl
iii) no girl
Also check weather the sum of these probabilities is 1.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Total number of family = 475 + 814 + 211 = 1500

i) number of families of 2 girls = 475

So, we get that,

P1 =$$\frac{Number of families having 2 girls}{Total number of family}$$
p =$$\frac{475}{1500} = \frac{19}{60}$$.

Therefore, the probability of a family, chosen at random, is having 2 girls

ii) Number of families having 1 girl = 814

So, we get that,

P2 = $$\frac{Number of families having 1 girls}{Total number of family}$$
p = $$\frac{814}{1500} = \frac{407}{750}$$..

Therefore, the probability of a family, chosen at random, is having 2 girls

iii) Number of families having no girl = 211
So, we get that,

$$P3 = \frac{Number of families having 0 girls}{Total number of family}$$
$$p = \frac{211}{1500}$$.

Therefore, the probability of a family, chosen at random, is having 2 girls

Now, Sum of all these probabilities
= P1 + P2 + P3
= $$\frac{19}{60} + \frac{407}{750} + \frac{211}{1500}$$
$$= \frac{475 + 814 + 211}{1500}$$
$$= \frac{1500}{1500} = 1$$

Hence, we can say that,
The sum of these probabilities is 1.

Q3 ) Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Number of students born in the month of August = 6
Total number of students = 40

$$P = \frac{Number of students born in August}{Total number of students}$$
$$P = \frac{6}{40} = \frac{3}{20}$$.

Therefore, the probability that a student of the class was born in August is $$\frac{3}{20}$$.

Q4 ) 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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Number of times 2 heads come up = 72
Total number Of times the coins were tossed = 200

$$P = \frac{Number of times 2 heads come up}{Total number of times the coins were tossed}$$
$$P = \frac{72}{200} = \frac{9}{25}$$

Therefore, the probability of 2 heads coming up is $$\frac{9}{25}$$.

Q5 ) 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:

Monthly Income (in Rs.)Vehicles per family
012Above 2
Less than 700010160250
7000 - 100000305272
10000 - 130001535291
1300 - 1600024695925
1600 or more15798288
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 I 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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

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 is $$P = \frac{579}{2400}$$

ii) Number Of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
Hence, required probability is $$P = \frac{10}{2400} =\frac{1}{240}$$

iii) Number of families earning less than Rs. 7000 per month and dcmas not own any vehicle = 10
Hence, required probability is $$P = \frac{10}{2400} =\frac{1}{240}$$

iv) Number of families earning Rs. 13000 - 16000 per month and owning more than 2 vehicles = 25
Hence, required probability is $$P = \frac{25}{2400} = \frac{1}{96}$$

v)Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 535 + 2 + 469 + 1 + 579 = 2062
Hence, required probability is $$P = \frac{2026}{2400} = \frac{1013}{1200}$$

Q6 ) Refer to Table 14.7, Chapter 14.
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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

i) Number of students obtained less than 20% in the mathematics test = 7

Total number of students = 90
Thus, $$P = \frac{7}{90}$$

Therefore, the probability that a student obtained less than 20% in the mathematics test is $$\frac{7}{90}$$.

ii) Number of students obtained 60 or above marks = 23
Total number of students = 90
Thus, $$P = \frac{23}{90}$$

Therefore, the probability that a student obtained marks 60 or above is $$\frac{23}{90}$$.

Q7 ) 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.

OpinionNumber of students
like135
Dislike65

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

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Total number of students
= 135 + 65 = 200

i) Number of students liking statistics = 135
$$P = \frac{135}{200} = \frac{27}{40}$$

Therefore, the probability of student liking statistics is $$\frac{27}{40}$$

ii) Thus, Probability of students that students dont like statistics is
$$= P = 1 - \frac{135}{200} = \frac{65}{200} = \frac{13}{40}$$

Therefore, the probability of student not liking statistics is $$\frac{13}{40}$$.

Q8 ) Refer to Q.2, Exercise 14.2. 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 $$\frac{1}{2}$$ km from her place of work?

NCERT Solutions for Class 9 Maths Chapter 15 Probability

i) Total number of engineers = 40
Also, Number of engineers living in less than 7 km from their place of work = 9
Hence, required probability that an engineer lives less than 7 km from her place =
$$P = \frac{9}{40}$$

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 =
$$P = \frac{31}{40}$$

iii)Hence, required probability that an engineer lives within $$\frac{1}{2}$$ km from her place of work is P = 0.

Q9 ) 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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Perform the activity by yourself and note down your observations.

Q10 ) 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 digits is divisible by 3.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Perform the activity by yourself and note down your observations.

Q11 ) 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.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Number of total bags = 11
Number of bags containing more than 5 kg of flour = 7
Hence, required probability = $$P = \frac{7}{11}$$

Therefore, the probability that any of these bags chosen at random contains more than 5 kg of flour is $$\frac{7}{11}$$.

Q12 ) In Q.5, Exercise 14.2, 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.

 Concentration of $$S\left(O_{2}\right)$$ (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

NCERT Solutions for Class 9 Maths Chapter 15 Probability

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 is $$P = \frac{2}{30} = \frac{1}{15}$$.

Therefore, the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days is $$\frac{1}{15}$$.

Q13 ) In Q.1, Exercise 14.2, 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.

 Blood Group Number of students O 12 A 9 B 6 AB 3

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Number of students having blood group AB = 3

Total number of students = 30
Hence, required probability is $$P = \frac{3}{30} = \frac{1}{10}$$.

Therefore, the probability that a student of this class, selected at random, has blood group AB is $$\frac{1}{10}$$.

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