Probability: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced PDF Download

 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