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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 probability of rolling a prime number on a fair six-sided die? |  |
Ans. To find the probability of rolling a prime number on a fair six-sided die, we first determine the total number of prime numbers on a die, which are 2, 3, and 5. Since there are 6 possible outcomes when rolling a die, the probability of rolling a prime number is 3/6 or 1/2.
| 2. If two cards are drawn at random from a standard deck of 52 cards without replacement, what is the probability that both cards are red? | |
Ans. When drawing two cards from a deck without replacement, there are 26 red cards out of the total 52 cards. The probability of drawing a red card on the first draw is 26/52. After drawing a red card, there are 25 red cards left out of 51 total cards. Therefore, the probability of drawing a second red card is 25/51. Multiplying these probabilities together gives us (26/52) * (25/51) = 25/102, which is the probability of drawing two red cards consecutively.
| 3. In a group of 10 people, what is the probability that at least two people have the same birthday? | |
Ans. The probability that no two people share the same birthday in a group of 10 can be calculated using the formula for permutations. We have 365 days in a year, so the probability that the first person has a unique birthday is 365/365. The second person must have a different birthday from the first, so the probability is 364/365. Continuing this pattern, the probability that all 10 people have different birthdays is (365/365) * (364/365) * ... * (356/365). The probability that at least two people share the same birthday is the complement of this probability, which is 1 - (365/365) * (364/365) * ... * (356/365).
| 4. A bag contains 4 red balls, 5 white balls, and 3 blue balls. If a ball is drawn at random from the bag, what is the probability that it is either red or white? | |
Ans. The total number of balls in the bag is 4 red + 5 white + 3 blue = 12 balls. The probability of drawing a red ball is 4/12 and the probability of drawing a white ball is 5/12. To find the probability of drawing either a red or white ball, we add the individual probabilities together, giving us 4/12 + 5/12 = 9/12 or 3/4.
| 5. If the probability of rain on any given day is 0.3, what is the probability of no rain for 5 consecutive days? | |
Ans. The probability of no rain on any given day is 0.7 (1 - 0.3). To find the probability of no rain for 5 consecutive days, we multiply the probability of no rain for each day together: (0.7)^5 = 0.16807. Therefore, the probability of no rain for 5 consecutive days is 0.16807.
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