R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 19 - Probability

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Chapter 19 - Probability Exercise Ex. 19

Question 1

A coin is tossed 500 times we get

Head: 285 times, Tail: 215 times.

When a coin is tossed at random, what is the probability of getting (i) A head? (ii) A tail?

Solution 1
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 2

12 packets of salt, each marked 2 kg, actually contained the following weights (in kg) of salt:

1.950, 2.020, 2.060, 1.980, 2.030, 1.970,

2.040, 1.990, 1.985, 2.025, 2.000, 1.980.

Out of these packets, one packet is chosen at random.

What is the probability that the chosen packet contains more than 2 kg of salt?

Solution 2

Total number of salt packets = 12

Number of packets containing more than 2 kg of salt = 5

Therefore, 

Probability that the chosen packet contains more than 2 kg of salt

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

 

Question 3

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he did not hit a boundary.

Solution 3

Total number of ball played = 30

Number of times boundary was hit = 6

Number of times boundary was not hit = 30 - 6 = 24

Therefore, 

Probability that the batsman did not hit the boundary

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 4

An organisation selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below:

Monthly income (in Rs.)

Number of vehicles per family

0

1

2

3 or more

Less than Rs.25000

10

160

25

0

Rs.25000 - Rs.30000

0

305

27

2

Rs.30000 - Rs.35000

1

535

29

1

Rs.35000 - Rs.40000

2

469

59

25

Rs.40000 or more

1

579

82

88

 

Suppose a family is chosen at random. Find the probability that the family chosen is

(i) earning Rs.25000 - Rs.30000 per month and owning exactly 2 vehicles.

(ii) earning Rs.40000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs.25000 per month and not owning any vehicle.

(iv) earning Rs.35000 - Rs.40000 per month and owning 2 or more vehicles.

(v) owning not more than 1 vehicle.

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 5

The table given below shows the mark obtained by 30 students in a test.

Marks

(Class interval)

1 - 10

11 - 20

21 - 30

31 - 40

41 - 50

Number of students

(Frequency)

7

10

6

4

3

 

Out of these students, one is chosen at random. What is the probability that the marks of the chosen student

(i) are 30 or less?

(ii) are 31 or more?

(iii) lie in the interval 21-30?

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 6

The table given shows the ages of 75 teachers in a school.

Age (in years)

18 - 29

30 - 39

40 - 49

50 - 59

Number of teachers

3

27

37

8

 

A teacher from this school is chosen at random. What is probability that the selected teacher is

(i) 40 or more than 40 years old?

(ii) of an age lying between 30-39 years (including both)?

(iii) 18 years or more and 49 years or less?

(iv) 18 years or more old?

(v) above 60 years of age?

NOTE Here 18 - 29 means 18 or more but less than or equal to 29.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 7

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Age

(in years)

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

Number of patients

90

50

60

80

50

30

 

One of the patients is selected at random.

What is probability that his age is

(i) 30 years or more but less than 40 years?

(ii) 50 years or more but less than 70 years?

(iii) 10 years or more but less than 40 years?

(iv) 10 years or more?

(v) less than 10 years?

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 8

The marks obtained by 90 students of a school in mathematics out of 100 are given as under:

Marks

0-20

20-30

30-40

40-50

50-60

60-70

70 and above

No. of students

7

8

12

25

19

10

9

 

From these students, a student is chosen at random.

What is the probability that the chosen student

(i) get 20% or less marks? (ii) get 60% or more marks?

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 9

It is known that a box of 800 electric bulbs contains 36 defective bulbs. One bulb is taken at random out of the box. What is probability that the bulb chosen is nondefective?

Solution 9

Total number of electric bulbs = 800

Number of defective bulbs = 36

Number of non-defective bulbs = 800 - 36 = 764

Hence, probability that the bulb chosen is non-defective

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 10

Fill in the blanks.

(i) Probability of an impossible event = ..... .

(ii) Probability of a sure event = ..... .

(iii) Let E be an event. Then, P(not E) = ..... .

(iv) P(E) + P(not E) = ..... .

(v) ..... ≤ P(E) ≤ .... .

Solution 10

Fill in the blanks.

(i) Probability of an impossible event = 0

(ii) Probability of a sure event = 1

(iii) Let E be an event. Then, P(not E) = 1 - P(E)

(iv) P(E) + P(not E) = 1

(v) 0 ≤ P(E) ≤ 1

Question 11

Two coin are tossed 400 times and we get

two heads:112 times; one head :160 times; 0 head :128 times.

When two coins are tossed at random, what is the probability of getting

(i) 2 heads? (ii)1 head? (iii)0 head?

Solution 11
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability
Question 12

Three coins are tossed 200 times and we get

three heads: 39 times; two heads: 58 times;

one head: 67 times; 0 head : 36 times.

When three coins are tossed at random, what is the probability of getting

(i) 3 heads? (ii) 1 head? (iii) 0 head? (iv) 2 heads?

Solution 12
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability
Question 13

A die is thrown 300 times and the outcomes are noted as given below:

Outcome

1

2

3

4

5

6

frequency

60

72

54

42

39

33

When a die is thrown at random, what is the probability of getting a

(i) 3? (ii) 6? (iii) 5? (iv)1?

Solution 13
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability



Question 14

In a survey of 200 ladies, it was found that 142 like coffee, while 58 dislike it.

Find the probability that a lady chosen at random

(i) Likes coffee (ii) dislikes coffee

Solution 14
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability
Question 15

The percentages of marks obtained by a student in six unit tests are given below :

Unit test

I

II

III

IV

V

VI

Percentageof marksobtained

53

72

28

46

67

59

 

A unit test is selected at random. What is the probability that the student gets more than 60% marks in the test?

Solution 15

Number of tests in which he gets more than60% marks =2

Total numbers of tests =6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - ProbabilityRequired probability

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 16

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under:

Type of vehicles

Two-wheelers

Three-wheelers

Four -wheelers

Frequency

84

68

88

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?

Solution 16
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 17

On one page of a telephone directory, there are 200 phone numbers. The frequency distribution of their units digits is given below:

Units digit

0

1

2

3

4

5

6

7

8

9

Frequency

19

22

23

19

21

24

23

18

16

15

One of the numbers is chosen at random from the page. What is the probability that the units digit of the chosen number is (i) 5? (ii) 8?

Solution 17
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

 

Question 18

The following table shows the blood groups of 40 students of the class.

Blood Group

A

B

O

AB

Number of students

11

9

14

6

One student of the class is chosen at random. What is the probability that the chosn student has blood group

(i) O? (ii) AB?

Solution 18
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Chapter 19 - Probability Exercise MCQ

Question 1

In a sample survey of 645 people, it was found that 516 people have a high school certificate. If a person is chosen at random, what is the probability that he/she has a high school certificate?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 1

Correct option: (d)

Total number of people = 645

Number of people having high school certificate = 516

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 2

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. What is the probability that in given throw, the ball does not hit the boundary?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 3

A bag contains 16 cards bearing number 1, 2, 3,…, 16 respectively. One card is chosen at random. What is the probability that the chosen card bears a number which is divisible by 3?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 4

A bag contains 5 red, 8 black and 7 white balls. One ball is chosen at random. What is the probability that the chosen ball is black

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 5

In 65 throws of a die, the outcomes were noted as under:

Outcomes

1

2

3

4

5

6

Number of times

8

10

12

16

9

10

A die is thrown at random. What is probability of getting a prime number

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 6

In 50 throws of a die, the outcomes were notes as under:

Outcome

1

2

3

4

5

6

Number of times

8

9

6

7

12

8

A die is thrown at random. What is the probability of getting an even number?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 7

The table given below shows the month of birth of 36 students of a class :

Month of birth

Jan

Feb

March

April

May

June

July

Aug

Sept

Oct

Nov

Dec

No.of students

4

3

5

0

1

6

1

3

4

3

4

2

A student is chosen at random from the class. What is the probability that the chosen student was born in October?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

 

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 8

Two coins are tossed simultaneously 600 times to get

2 heads: 234 times, 1 head: 206 times, 0 head: 160 times.

If two coins are tossed at random, what is the probability of getting at least one head?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 8

Correct option: (c)

Total number of outcomes = 600

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 9

In a medical examination of students of a class, the following blood groups are recorded:

Blood group

A

B

AB

O

Number of students

11

15

8

6

 

From this class, a student is chosen at random. What is the probability that the chosen student has blood group AB?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 9

Correct option: (c)

Total number of students = 11 + 15 + 8 + 6 = 40

Number of students having blood group AB = 8 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 10

80 bulbs are selected at random from a lot and their lifetime in hours is recorded as under.

Lifetime (in hours)

300

500

700

900

1100

Frequency

10

12

23

25

10

 

One bulb is selected at random from the lot. What is the probability that its life is 1150 hours?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) 1

(d) 0

Solution 10

Correct option: (d)

Total number of bulbs = 80

Number of bulbs having life of 1150 hours = 0

Required probability = 0 

Question 11

In a survey of 364 children aged 19 - 36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 11

Correct option: (c)

Total number of children = 364

Number of children who like to eat potato chips = 91

Number of children who do not like to eat potato chips = 364 - 91 = 273

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 12

Two coins are tossed 1000 times and the outcomes are recorded as given below:

Number of heads

2

1

0

Frequency

200

550

250

 

Now, if two coins are tossed at random, what is the probability of getting at most one head?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 12

Correct option: (b)

Total number of outcomes = 1000

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 13

80 bulbs are selected at random from a lot and their lifetime in hours is recorded as under.

Lifetime (in hours)

300

500

700

900

1100

Frequency

10

12

23

25

10

 

One bulb is selected at random from the lot. What is the probability that selected bulb has a life more than 500 hours?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 13

Correct option: (b)

Total number of bulbs = 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 14

To know the opinion of the students about the subject Sanskrit, a survey of 200 students was conducted. The data is recorded as under.

Opinion

like

dislike

Number of students

135

65

 

What is the probability that a student chosen at random does not like it?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 14

Correct option: (c)

Total number of students = 200

Number of students who does not like Sanskrit = 65

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability 

Question 15

A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability

Question 16

It is given that the probability of winning a game is 0.7. What is the probability of losing the game?

(a) 0.8

(b) 0.3

(c) 0.35

(d) 0.15

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Probability