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
Answer :
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,
Therefore, the probability that she did not hit a boundary is
Q2 )
1500 families with 2 children were selected randomly, and the following data were
recorded:
No. of girls in a family | 2 | 1 | 0 |
---|---|---|---|
No. of families | 475 | 814 | 211 |
NCERT Solutions for Class 9 Maths Chapter 15 Probability
Answer :
Total number of family = 475 + 814 + 211 = 1500
i) number of families of 2 girls = 475
So, we get that,
P1 =
p =
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 =
p =
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,
Therefore, the probability of a family, chosen at random, is having 2 girls
Now, Sum of all these probabilities
= P1 + P2 + P3
=
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
Answer :
Number of students born in the month of August = 6
Total number of students = 40
Therefore, the probability that a student of the class was born in August is
Q4 )
Three coins are tossed simultaneously 200 times with the following frequencies of
different outcomes:
Outcome | 3 heads | 2 heads | 1 heads | 0 head |
---|---|---|---|---|
Frequency | 23 | 72 | 77 | 28 |
NCERT Solutions for Class 9 Maths Chapter 15 Probability
Answer :
Number of times 2 heads come up = 72
Total number Of times the coins were tossed = 200
Therefore, the probability of 2 heads coming up is
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 | |||
---|---|---|---|---|
0 | 1 | 2 | Above 2 | |
Less than 7000 | 10 | 160 | 25 | 0 |
7000 - 10000 | 0 | 305 | 27 | 2 |
10000 - 13000 | 1 | 535 | 29 | 1 |
1300 - 16000 | 2 | 469 | 59 | 25 |
1600 or more | 1 | 579 | 82 | 88 |
NCERT Solutions for Class 9 Maths Chapter 15 Probability
Answer :
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
ii) Number Of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
Hence, required probability is
iii) Number of families earning less than Rs. 7000 per month and dcmas not own any vehicle = 10
Hence, required probability is
iv) Number of families earning Rs. 13000 - 16000 per month and owning more than 2 vehicles = 25
Hence, required probability is
v)Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 535 + 2 + 469 + 1 + 579 = 2062
Hence, required probability is
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
Answer :
i) Number of students obtained less than 20% in the mathematics test = 7
Total number of students = 90
Thus,
Therefore, the probability that a student obtained less than 20% in the mathematics test is
ii) Number of students obtained 60 or above marks = 23
Total number of students = 90
Thus,
Therefore, the probability that a student obtained marks 60 or above is
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.
Opinion | Number of students |
---|---|
like | 135 |
Dislike | 65 |
NCERT Solutions for Class 9 Maths Chapter 15 Probability
Answer :
Total number of students
= 135 + 65 = 200
i) Number of students liking statistics = 135
Therefore, the probability of student liking statistics is
ii) Thus, Probability of students that students dont like statistics is
Therefore, the probability of student not liking statistics is
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
NCERT Solutions for Class 9 Maths Chapter 15 Probability
Answer :
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 =
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)Hence, required probability that an engineer lives within
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
Answer :
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
Answer :
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
Answer :
Number of total bags = 11
Number of bags containing more than 5 kg of flour = 7
Hence, required probability =
Therefore, the probability that any of these bags chosen at random contains more than 5 kg of flour is
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 | 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
Answer :
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
Therefore, the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days is
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
Answer :
Number of students having blood group AB = 3
Total number of students = 30
Hence, required probability is
Therefore, the probability that a student of this class, selected at random, has blood group AB is