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Page 1
JEE Mains Previous Year Questions
(2021-2024): Probability
2024
Q1 - 2024 (01 Feb Shift 1)
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at
random without replacement and it was found that 2 balls are white and other 2 balls are
black. The probability that the bag contains equal number of white and black balls is:
(1)
2
5
(2)
2
7
(3)
1
7
(4)
1
5
Q2 - 2024 (01 Feb Shift 2)
Let Ajay will not appear in JEE exam with probability p =
2
7
, while both Ajay and Vijay will
appear in the exam with probability ?? =
1
5
. Then the probability, that Ajay will appear in
the exam and Vijay will not appear is :
(1)
9
35
(2)
18
35
(3)
24
35
(4)
3
35
Q3 - 2024 (27 Jan Shift 1)
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses
required and let ?? = ?? (?? = 3), ?? = ?? (?? = 3) and ?? = P(X = 6 | X > 3). Then
b+c
a
is equal
to
Page 2
JEE Mains Previous Year Questions
(2021-2024): Probability
2024
Q1 - 2024 (01 Feb Shift 1)
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at
random without replacement and it was found that 2 balls are white and other 2 balls are
black. The probability that the bag contains equal number of white and black balls is:
(1)
2
5
(2)
2
7
(3)
1
7
(4)
1
5
Q2 - 2024 (01 Feb Shift 2)
Let Ajay will not appear in JEE exam with probability p =
2
7
, while both Ajay and Vijay will
appear in the exam with probability ?? =
1
5
. Then the probability, that Ajay will appear in
the exam and Vijay will not appear is :
(1)
9
35
(2)
18
35
(3)
24
35
(4)
3
35
Q3 - 2024 (27 Jan Shift 1)
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses
required and let ?? = ?? (?? = 3), ?? = ?? (?? = 3) and ?? = P(X = 6 | X > 3). Then
b+c
a
is equal
to
Q4 - 2024 (27 Jan Shift 2)
An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made
without replacement. The probability, that the first draw gives all white balls and the
second draw gives all black balls, is :
(1)
5
256
(2)
5
715
(3)
3
715
(4)
3
256
Q5 - 2024 (29 Jan Shift 1)
A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number
of throws , is
(1)
5
6
(2)
1
6
(3)
5
11
(4)
6
11
Q6 - 2024 (29 Jan Shift 2)
An integer is chosen at random from the integers 1,2,3, … ,50. The probability that the
chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1)
8
25
(2)
21
50
(3)
9
50
(4)
14
25
Page 3
JEE Mains Previous Year Questions
(2021-2024): Probability
2024
Q1 - 2024 (01 Feb Shift 1)
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at
random without replacement and it was found that 2 balls are white and other 2 balls are
black. The probability that the bag contains equal number of white and black balls is:
(1)
2
5
(2)
2
7
(3)
1
7
(4)
1
5
Q2 - 2024 (01 Feb Shift 2)
Let Ajay will not appear in JEE exam with probability p =
2
7
, while both Ajay and Vijay will
appear in the exam with probability ?? =
1
5
. Then the probability, that Ajay will appear in
the exam and Vijay will not appear is :
(1)
9
35
(2)
18
35
(3)
24
35
(4)
3
35
Q3 - 2024 (27 Jan Shift 1)
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses
required and let ?? = ?? (?? = 3), ?? = ?? (?? = 3) and ?? = P(X = 6 | X > 3). Then
b+c
a
is equal
to
Q4 - 2024 (27 Jan Shift 2)
An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made
without replacement. The probability, that the first draw gives all white balls and the
second draw gives all black balls, is :
(1)
5
256
(2)
5
715
(3)
3
715
(4)
3
256
Q5 - 2024 (29 Jan Shift 1)
A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number
of throws , is
(1)
5
6
(2)
1
6
(3)
5
11
(4)
6
11
Q6 - 2024 (29 Jan Shift 2)
An integer is chosen at random from the integers 1,2,3, … ,50. The probability that the
chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1)
8
25
(2)
21
50
(3)
9
50
(4)
14
25
Q7 - 2024 (30 Jan Shift 1)
Two integers x and y are chosen with replacement from the set {0,1,2,3, … ,10}. Then the
probability that |?? - ?? | > 5 is :
(1)
30
121
(2)
62
121
(3)
60
121
(4)
31
121
Q8 - 2024 (31 Jan Shift 1)
Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is
selected at random and a ball is drawn from it. The probability of drawing the ball from
the bag ?? , if the ball drawn in white, is :
(1)
1
4
(2)
1
9
(3)
1
3
(4)
3
10
Q9 - 2024 (31 Jan Shift 1)
Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue
and 15 orange marbles, with replacement being made after each drawing. Then the
probability, that first drawn marble is red and second drawn marble is white, is
(1)
2
25
(2)
4
25
(3)
2
3
(4)
4
75
Q10 - 2024 (31 Jan Shift 1)
Three rotten apples are accidently mixed with fifteen good apples. Assuming the random
variable ?? to be the number of rotten apples in a draw of two apples, the variance of ?? is
Page 4
JEE Mains Previous Year Questions
(2021-2024): Probability
2024
Q1 - 2024 (01 Feb Shift 1)
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at
random without replacement and it was found that 2 balls are white and other 2 balls are
black. The probability that the bag contains equal number of white and black balls is:
(1)
2
5
(2)
2
7
(3)
1
7
(4)
1
5
Q2 - 2024 (01 Feb Shift 2)
Let Ajay will not appear in JEE exam with probability p =
2
7
, while both Ajay and Vijay will
appear in the exam with probability ?? =
1
5
. Then the probability, that Ajay will appear in
the exam and Vijay will not appear is :
(1)
9
35
(2)
18
35
(3)
24
35
(4)
3
35
Q3 - 2024 (27 Jan Shift 1)
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses
required and let ?? = ?? (?? = 3), ?? = ?? (?? = 3) and ?? = P(X = 6 | X > 3). Then
b+c
a
is equal
to
Q4 - 2024 (27 Jan Shift 2)
An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made
without replacement. The probability, that the first draw gives all white balls and the
second draw gives all black balls, is :
(1)
5
256
(2)
5
715
(3)
3
715
(4)
3
256
Q5 - 2024 (29 Jan Shift 1)
A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number
of throws , is
(1)
5
6
(2)
1
6
(3)
5
11
(4)
6
11
Q6 - 2024 (29 Jan Shift 2)
An integer is chosen at random from the integers 1,2,3, … ,50. The probability that the
chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1)
8
25
(2)
21
50
(3)
9
50
(4)
14
25
Q7 - 2024 (30 Jan Shift 1)
Two integers x and y are chosen with replacement from the set {0,1,2,3, … ,10}. Then the
probability that |?? - ?? | > 5 is :
(1)
30
121
(2)
62
121
(3)
60
121
(4)
31
121
Q8 - 2024 (31 Jan Shift 1)
Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is
selected at random and a ball is drawn from it. The probability of drawing the ball from
the bag ?? , if the ball drawn in white, is :
(1)
1
4
(2)
1
9
(3)
1
3
(4)
3
10
Q9 - 2024 (31 Jan Shift 1)
Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue
and 15 orange marbles, with replacement being made after each drawing. Then the
probability, that first drawn marble is red and second drawn marble is white, is
(1)
2
25
(2)
4
25
(3)
2
3
(4)
4
75
Q10 - 2024 (31 Jan Shift 1)
Three rotten apples are accidently mixed with fifteen good apples. Assuming the random
variable ?? to be the number of rotten apples in a draw of two apples, the variance of ?? is
(1)
37
153
(2)
57
153
(3)
47
153
(4)
40
153
Q11 - 2024 (31 Jan Shift 2)
A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3
times, then the probability of getting two tails and one head is-
(1)
2
9
(2)
1
9
(3)
2
27
(4)
1
27
Answer Key
Solutions
Q1
P(4 W4 B/2 W2 B) =
?? (4?? 4?? ) × ?? (2?? 2?? /4?? 4?? )
?? (2?? 6?? ) × ?? (2?? 2?? /2?? 6?? ) + ?? (3?? 5?? ) × ?? (2?? 2?? /3?? 5?? )
¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯
+ ? … … + ?? (6?? 2?? ) × ?? (2?? 2?? /6?? 2?? )
Page 5
JEE Mains Previous Year Questions
(2021-2024): Probability
2024
Q1 - 2024 (01 Feb Shift 1)
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at
random without replacement and it was found that 2 balls are white and other 2 balls are
black. The probability that the bag contains equal number of white and black balls is:
(1)
2
5
(2)
2
7
(3)
1
7
(4)
1
5
Q2 - 2024 (01 Feb Shift 2)
Let Ajay will not appear in JEE exam with probability p =
2
7
, while both Ajay and Vijay will
appear in the exam with probability ?? =
1
5
. Then the probability, that Ajay will appear in
the exam and Vijay will not appear is :
(1)
9
35
(2)
18
35
(3)
24
35
(4)
3
35
Q3 - 2024 (27 Jan Shift 1)
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses
required and let ?? = ?? (?? = 3), ?? = ?? (?? = 3) and ?? = P(X = 6 | X > 3). Then
b+c
a
is equal
to
Q4 - 2024 (27 Jan Shift 2)
An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made
without replacement. The probability, that the first draw gives all white balls and the
second draw gives all black balls, is :
(1)
5
256
(2)
5
715
(3)
3
715
(4)
3
256
Q5 - 2024 (29 Jan Shift 1)
A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number
of throws , is
(1)
5
6
(2)
1
6
(3)
5
11
(4)
6
11
Q6 - 2024 (29 Jan Shift 2)
An integer is chosen at random from the integers 1,2,3, … ,50. The probability that the
chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1)
8
25
(2)
21
50
(3)
9
50
(4)
14
25
Q7 - 2024 (30 Jan Shift 1)
Two integers x and y are chosen with replacement from the set {0,1,2,3, … ,10}. Then the
probability that |?? - ?? | > 5 is :
(1)
30
121
(2)
62
121
(3)
60
121
(4)
31
121
Q8 - 2024 (31 Jan Shift 1)
Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is
selected at random and a ball is drawn from it. The probability of drawing the ball from
the bag ?? , if the ball drawn in white, is :
(1)
1
4
(2)
1
9
(3)
1
3
(4)
3
10
Q9 - 2024 (31 Jan Shift 1)
Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue
and 15 orange marbles, with replacement being made after each drawing. Then the
probability, that first drawn marble is red and second drawn marble is white, is
(1)
2
25
(2)
4
25
(3)
2
3
(4)
4
75
Q10 - 2024 (31 Jan Shift 1)
Three rotten apples are accidently mixed with fifteen good apples. Assuming the random
variable ?? to be the number of rotten apples in a draw of two apples, the variance of ?? is
(1)
37
153
(2)
57
153
(3)
47
153
(4)
40
153
Q11 - 2024 (31 Jan Shift 2)
A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3
times, then the probability of getting two tails and one head is-
(1)
2
9
(2)
1
9
(3)
2
27
(4)
1
27
Answer Key
Solutions
Q1
P(4 W4 B/2 W2 B) =
?? (4?? 4?? ) × ?? (2?? 2?? /4?? 4?? )
?? (2?? 6?? ) × ?? (2?? 2?? /2?? 6?? ) + ?? (3?? 5?? ) × ?? (2?? 2?? /3?? 5?? )
¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯
+ ? … … + ?? (6?? 2?? ) × ?? (2?? 2?? /6?? 2?? )
=
1
5
×
4
C
2
×
4
C
2
8
C
4
1
5
×
2
C
2
×
6
C
2
8
C
4
+
1
5
×
3
C
2
×
5
C
2
8
C
4
+ ? +
1
5
×
6
C
2
×
2
C
2
8
C
4
=
2
7
Q2
P(A
¯
) =
2
7
= p
P(A n V) =
1
5
= q
P(A) =
5
7
Ans. ?? (?? n ?? ?
) =
18
35
Q3
a = P(X = 3) =
5
6
×
5
6
×
1
6
=
25
216
b = P(X = 3) =
5
6
×
5
6
×
1
6
+ (
5
6
)
3
·
1
6
+ (
5
6
)
4
·
1
6
+ ? …
=
25
216
1 -
5
6
=
25
216
×
6
1
=
25
36
?? (?? = 6) = (
5
6
)
5
·
1
6
+ (
5
6
)
6
·
1
6
+ ? ….
=
(
5
6
)
5
·
1
6
1 -
5
6
= (
5
6
)
5
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209 videos|443 docs|143 tests
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FAQs on Probability: JEE Mains Previous Year Questions (2021-2024) - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the basic concept of probability in JEE Mains? |  |
Ans. Probability in JEE Mains deals with the likelihood of an event occurring, which is expressed as a number between 0 and 1. It is used to analyze random experiments and predict the likelihood of various outcomes.
| 2. How is probability calculated in JEE Mains? | |
Ans. In JEE Mains, probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio gives the probability of an event occurring.
| 3. What are the different types of probability questions asked in JEE Mains? | |
Ans. JEE Mains may include questions on classical probability, conditional probability, independent events, Bayes' theorem, and permutations and combinations. Students are required to apply these concepts to solve probability problems.
| 4. How can I improve my probability-solving skills for JEE Mains? | |
Ans. To improve probability-solving skills for JEE Mains, practice solving a variety of probability problems from previous year papers and mock tests. Understanding the concepts thoroughly and practicing regularly can enhance your problem-solving abilities.
| 5. Are there any specific strategies to tackle probability questions in JEE Mains? | |
Ans. One strategy to tackle probability questions in JEE Mains is to break down the problem into smaller parts and apply the relevant probability concepts to each part. Additionally, drawing diagrams or using visual aids can help in understanding the problem better and arriving at the correct solution.
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