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

## Chapter 19 – Probability Exercise Ex. 19

_{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?}

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?

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

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.

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

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 | Number | |||

0 | 1 | 2 | 3 | |

Less | 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.

The table given below shows the

mark obtained by 30 students in a test.

Marks (Class | 1 | 11 | 21 | 31 | 41 |

Number (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?

The table given shows the ages of

75 teachers in a school.

Age | 18 | 30 | 40 | 50 |

Number | 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.

Following are the ages (in years)

of 360 patients, getting medical treatment in a hospital:

Age (in | 10 | 20 | 30 | 40 | 50 | 60 |

Number | 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?

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?

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?

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

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) ≤ …. .

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__

_{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?}

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?

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?

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

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?

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

Total numbers of tests =6

Required probability

_{}

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?

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?

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?

## Chapter 19 – Probability Exercise MCQ

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)

(b)

(c)

(d)

Correct

option: (d)

Total

number of people = 645

Number

of people having high school certificate = 516

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?

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?

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

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

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?

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?

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)

(b)

(c)

(d)

Correct

option: (c)

Total

number of outcomes = 600

In a medical examination of students of a class, the

following blood groups are recorded:

Blood | A | B | AB | O |

Number of | 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)

(b)

(c)

(d)

Correct

option: (c)

Total

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

Number

of students having blood group AB = 8

80 bulbs are selected at random from a lot and their

lifetime in hours is recorded as under.

Lifetime | 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)

(b)

(c) 1

(d) 0

Correct

option: (d)

Total

number of bulbs = 80

Number

of bulbs having life of 1150 hours = 0

∴ Required

probability = 0

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)

(b)

(c)

(d)

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

Two coins are tossed 1000 times and the outcomes are

recorded as given below:

Number of | 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)

(b)

(c)

(d)

Correct

option: (b)

Total

number of outcomes = 1000

80 bulbs are selected at random from a lot and their

lifetime in hours is recorded as under.

Lifetime | 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)

(b)

(c)

(d)

Correct

option: (b)

Total

number of bulbs = 80

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 | 135 | 65 |

What is the probability that a student chosen at random

does not like it?

(a)

(b)

(c)

(d)

Correct

option: (c)

Total

number of students = 200

Number

of students who does not like Sanskrit = 65

A coin is tossed 60 times and the tail appears 35

times. What is the probability of getting a head?

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