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Probability MATHS - Probability

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 33 questions in this chapter.

Question types

Probability question types

33 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

33
Questions
5
Question groups
5
Question types
Sample Questions

Probability questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
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 the selected bulb has a life more than 500 hours?
  1. $\frac{27}{40}$
  2. $\frac{29}{40}$
  3. $\frac{5}{16}$
  4. $\frac{11}{40}$
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Q 2M.C.Q1 Mark
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?
  1. $\frac{103}{300}$
  2. $\frac{39}{100}$
  3. $\frac{11}{15}$
  4. $\frac{4}{15}$
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Q 3M.C.Q1 Mark
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:
  1. $\frac{1}{4}$
  2. $\frac{1}{2}$
  3. $\frac{3}{4}$
  4. $\frac{4}{5}$
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Q 4M.C.Q1 Mark
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?
  1. $\frac{13}{20}$
  2. $\frac{3}{8}$
  3. $\frac{1}{5}$
  4. $\frac{11}{40}$
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Q 5M.C.Q1 Mark
It is given that the probability of winning a game is 0.7. What is the probability of losing the game?
  1. 0.8
  2. 0.3
  3. 0.35
  4. 0.15
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Q 62 Marks Questions2 Marks
The percentages of marks obtained by a student in six unit tests are given below:
Unit test
 $I$ $II$ $III$ $IV$ $V$ $VI$
Percentage of marks obtained
 $53$ $72$ $28$ $46$ $67$ $59$
A unit test is selected at random. What is the probability that the student gets more than $60\%$ marks in the test?
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Q 72 Marks Questions2 Marks
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
Number 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:
  1. Gets 20% or less marks?
  2. Gets 60% or more marks?
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Q 82 Marks Questions2 Marks
12 Packets of salt, each marked 2kg, 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 2kg of salt?
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Q 92 Marks Questions2 Marks
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:
Types of vehicle
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?
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Q 113 Marks Question3 Marks
On one page of a telephone directory, there are $200$ phone numbers. The frequency distribution of their unit's digits is given below:
Unit's 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 unit's digit of the chosen number is:
  1. $5?$
  2. $8?$
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Q 123 Marks Question3 Marks
The following table shows the blood groups of $40$ students of a 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 chosen students blood group is:
$i. O? \ \ \ \ \  ii. AB?$
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Q 133 Marks Question3 Marks
The table given below shows the marks 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:
  1. Are 30 or less?
  2. Are 31 or more?
  3. Lie in the interval 21 - 30?
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Q 143 Marks Question3 Marks
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.
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Q 155 Marks Questions5 Marks
The table given below 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 the probability that the selected teacher is:
  1. 40 or more than 40 years old?
  2. Of an age lying between 30 - 39 years (including both)?
  3. 18 years or more and 49 years or less?
  4. 18 years or more old?
  5. Above 60 years of age?
Note: Here 18 - 29 means 18 or more but less than or equal to 29.
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Q 165 Marks Questions5 Marks
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 the probability that his age is:
  1. 30 years or more but less than 40 years?
  2. 50 years or more but less than 70 years?
  3. 10 years or more but less than 40 years?
  4. 10 years or more?
  5. Less than 10 years?
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Q 175 Marks Questions5 Marks
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 ₹)
Number of vehicles per family
0
1
2
3 or more
Less than ₹ 25000
10
160
25
0
 ₹ 25000 - ₹ 30000
0
305
27
2
 ₹ 30000 - ₹ 35000
1
535
29
1
 ₹ 35000 - ₹ 40000
2
469
59
25
 ₹ 40000 or more
1
579
82
88
Suppose a family is chosen at random. Find the probability that the family chosen is:
  1. Earning ₹ 25000 - ₹ 30000 per month and owning exactly 2 vehicles.
  2. Earning ₹ 40000 or more per month and owning exactly 1 vehicle.
  3. Earning less than ₹ 25000 per month and not owning any vehicle.
  4. Earning ₹ 35000 - ₹ 40000 per month and owning 2 or more vehicles.
  5. Owning not more than 1 vehicle.
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Q 184 Marks Questions4 Marks
Two coins 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
  1. $2$ heads?
  2. $1$ heads?
  3. $0$ heads?
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Q 194 Marks Questions4 Marks
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 dice is thrown at random, what is the probability of getting a
  1. $3$?
  2. $6$?
  3. $5$?
  4. $1$?
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Q 204 Marks Questions4 Marks
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
  1. $3$ heads?
  2. $1$ heads?
  3. $0$ heads?
  4. $2$ heads?
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