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 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.
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 2130?
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 3039 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 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?
The marks obtained by 90 students of a school in mathematics out of 100 are given as under:
Marks 
020 
2030 
3040 
4050 
5060 
6070 
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 nondefective bulbs = 800  36 = 764
Hence, probability that the bulb chosen is nondefective
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 
Twowheelers 
Threewheelers 
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 twowheeler?
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 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)
(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 (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)
(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 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)
(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 (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)
(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 students 
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
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