Notes
Ncert Solutions
Assignments
Revision sheet
Given below are the Class 9 Maths Assignments for Probability
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
f) Link type comprehension
1) 1000 families with 2 children were selected randomly and the following data were recorded:
No. of boys in family

0

1

2

No. of families:

240

560

200

If a family is chosen at random, find the probability that it has
 No boy
 One boy
 2 boys
 at least one boy
 at most 1 boy
2) The percentage of marks obtained by a student in the monthly unit tests are given below:
Unit Test:

I

II

III

IV

V

Percentage of marks obtained:

58

74

76

62

85

Find the probability that the students gets:
 a first class i.e. at least 60% marks
 marks between 70% and 80%
 a distinction i.e. 75% or above
 less than 65% marks
3) On the page of a telephone directory, there were 200 telephone numbers. The frequency distribution of their unit place digit(for example, in the number 55828573, the unit place is 3) is given in the table below
Digits:

0

1

2

3

4

5

6

7

8

9

Frequency

22

26

22

22

20

10

14

28

16

20

A no. is chosen at random, find the probability that the digit at the unit’s place is:
 9
 a non zero multiple of 3
 a non zero even no.
 an odd no.
4) A tyre manufacturing company kept a record of the distance covered before a tyre to be replaced. Following table shows the results of 1000 cases
Distances in km

no. of tyres

less than 400

210

400 – 900

325

900 – 1400

385

more than 1400

80

If you buy a tyre of this company, what is the probability that:
 it will need to be replaced before it has covered 400km?
 it will last more than 900 km?
 it will need to be replaced after it has covered somewhere between 400km an 1400km?
 it will not need to be replaced at all?
 it will need to be replaced?
5) Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardized conditions favorable to germination. After 20 days the number of seeds which had germinated in each collection were counted and recorded as follows
Bag:

1

2

3

4

5

No. of seeds germinated

40

48

42

39

41

What is the probability of germination of:
 more than 40 seeds in a bag?
 49 seeds in a bag?
 More than 35 seeds in a bag?
 at least 40 seeds in a bag?
 at most 40 seeds in a bag?
6) The distances (in km) of 40 female engineers from the residence to their place of work were found as follows:
5

3

10

20

25

11

13

7

12

32

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

2

Find the probability that the engineer lives:
 less than 7km from her place of work?
 at least 7km from her place of work?
 Within 1/2km from her place of work?
 at most 15km from her place of work?
7) Following table shows the marks scored by a group of 90 students in a mathematics test of 100 marks.
Marks:

020

2030

3040

4050

5060

6070

70100

No. of students:

7

10

10

20

15

8

20

Find the probability that the student obtains
a) less than 20
b} 60 or more
8) Following frequency distribution gives the weight of 38 students of a class:
Weight

No. Of students

Weight

No. Of students

3135

9

5660

2

3640

5

6165

2

4145

14

6670

1

4650

3

7175

1

5155

1



Find the probability that weight of the students in the class is:
 at most 60kg
 at least 36kg
 not more than 50kg
 Also define two events in this context, one having probability 0 and other having 1.
9) An insurance company selected 2000 drivers at random in a particular city to find a relationship return age and accidents. The data obtained are given in the following table:
Age of drivers

Accidents in one year

0

1

2

3

Over 3

1829

440

160

110

61

35

3050

505

125

60

22

18

Above 50

360

45

35

15

9

Find the probabilities of following events for a driver chosen at random from the life city:
 being 1829 year of age and having exactly 3 accidents in one year.
 being 3050 years of age and having one or more accidents in a year.
 having no accidents in one year
10) A recent survey found that the ages fo workers in a factory is distributed as follows:
Ages

2029

3039

4049

5059

60 and above

No of workers

38

27

86

46

3

if a person is selected at randomly, find the probability that a person is
a) 40 yrs or more
b) under 40 yrs
c) having age from 30 to 39 yrs
d) under 60 but over 39
11) The blood groups of 30 students of class IX are recorded as follows:
A, B, O, O, AB, O, A, O, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
A student is selected at random from the class for blood donation. Find the probability that the blood group of student chosen is
a) A
b) B
c) AB
d) O
12) A company selected 2400 families at random and surveys them to determine a relationship between income level and the no. of vehicles in a home. 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

700010000

0

305

27

2

1000013000

1

535

29

1

1300016000

2

469

29

25

16000 o more

1

579

82

88

If a family is chosen at random, find the probability that the family is
 earning Rs 1000013000 month and owing exactly 2 vehicles.
 earning Rs 16000 or more per month and owing exactly 1 vehicle.
 earning less than R 7000 per month and does not own any vehicle.
 earning Rs 1300016000 month and owing more than 2 vehicles.
 owning not more than 1 vehicle
 owning at least one vehicle.
13) The following table gives the life time of 400 neon lamps:
Lifetime (in hrs)

no. of lamps

300400

14

400500

56

500600

60

600700

86

700800

74

800900

62

9001000

48

A bulb is selected at random. Find the probability that the life time of selected bulb is:
 less than 400
 between 300800hrs
 at least 700 hrs
14) Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:
Wages

No. Of workers

Wages

No. Of workers

110130

3

190210

5

130150

4

210230

4

150170

5

230250

3

170190

6



A worker is selected at random. Find the probability that his wages are:
 less than Rs 150
 at least Rs 210
 more than or equal to 150 but less than Rs 210.
15) If the probability of winning a Hockey match is one half more than twice of probability of losing the match, find the probabilities of
 winning of the match
 losing of the match
16) The probability of guessing the correct answer to a certain questions . If the probability of not guessing the correct answer is then find the value of x.
17) If the difference between the probability of success and failure of an event is 5/19, find the probabilities of success and failure of an event.
18) The probability of guessing the correct answer to a certain question is .If the probability of not guessing the correct answer is then find the value of x.
19) It the probability of winning a race of an athlete is 1/6 less than twice the probability of losing the race, find the probability of winning the race.
20) The following table shows the daily production of TV sets in a industry for 7 days of a week.
Day

Mon

Tue

Wed

Thu

Fri

Sat

Sun

No. of TV

300

400

150

250

100

350

200

If a TV is selected at random, find the probability that it is selected
 from a day having maximum production
 from a day having minimum production
 from Saturday’s production
22) A parent has collected data of number of school based on the monthly fees, so that he can choose the school for admission of his child. Data is as under:
Fee (in Rs)

300600

600900

9001200

12001500

15001800

18002100

21002400

No. of schools

5

12

14

18

10

9

4

If a school is selected at random, find the probability that the school is having –
 minimum fees
 maximum fees
 fees less than 2900
 fees at least Rs 1500
23) A survey of 2000 people of different age groups was conduct to find out their preference n watching different types of movies.
Type I – family
Type II – comedy & family
Type III – romantic, comedy & family
Type IV – action, romantic, comedy & family
The data recorded was as follows –
Age group
(in years)

Type I

Type II

Type III

Type IV

All

1829

440

160

110

61

35

3050

505

125

60

22

18

Above 50

360

45

35

15

9

Find the probability that person chosen at random is
 in 1829 years of age and likes type II movies
 above 50 years of age and likes all types of movies
 in 3050 years and likes type I movies.
24) An insurance company selected 2000 drivers at random in a particular city to find a relationship between age and accidents. The data obtained are given in following table
Age groups of no. of accidents
Drivers (in years) 0 1 2 3 more than 3
1829 440 160 110 61 35
3050 505 125 60 21 18
above 50 360 45 35 15 10
Find the probability:
 being 1829 years of age and having exactly 3 accidents.
 being 3050 years of age and having one or more accidents in a year.
 having no accidents in 1 year.
 which value would you like to remember from data?
25) Find the probability that a leap year, selected at random will have 53 Sundays
26) A coin is tossed 15 times and observed that 11 times head comes up. Find the probability that a tail comes up
Class 9 Maths Home page
Class 9 Science Home page