Revision Super Set – Probability Class 12 CBSE 2026

Welcome to the ultimate Revision Super Set – Probability for Class 12 CBSE 2026. This set contains 120 carefully curated questions covering all important probability concepts, including basic probability, conditional probability, random variables, binomial, Poisson, and normal distributions. Whether you are preparing for board exams or competitive tests, this revision guide will help you strengthen your understanding and boost confidence.

Part A: Basic & Conditional Probability (Q1–40)

This section covers fundamental probability concepts, including single and multiple events, dice, coins, and card problems. Practice these questions to master the basics before moving to distributions.

1. A die is rolled once. Find the probability of getting a prime number.
2. Two coins are tossed. Find the probability of getting at least one head.
3. A card is drawn from a well-shuffled deck. Find the probability of drawing a black face card.
4. Two dice are rolled. Find the probability that the sum is 7.
5. A box contains 5 red and 3 blue balls. A ball is drawn at random. Find the probability that it is red.
6. Two dice are thrown. Find the probability that the numbers obtained are equal.
7. A bag contains 6 white and 4 black balls. Two balls are drawn without replacement. Find the probability both are black.
8. A family has two children. Find the probability that both are girls.
9. A box contains 10 balls numbered 1–10. One ball is drawn at random. Find the probability that the number is divisible by 3.
10. If \(P(A) = 0.5\) and \(P(B) = 0.4\), find the maximum and minimum values of \(P(A \cap B)\).
11. In a deck of 52 cards, find the probability of drawing a heart or a king.
12. A bag contains 7 red and 5 green balls. Two balls are drawn with replacement. Find the probability both are red.
13. A die is rolled twice. Find the probability of getting a sum less than 5.
14. Two dice are thrown. Find the probability of getting at least one 6.
15. A box contains 4 white, 3 red, and 3 blue balls. One ball is drawn at random. Find the probability it is not blue.
16. A bag contains 3 black and 7 white balls. Two balls are drawn without replacement. Find the probability that one is black and one is white.
17. Three coins are tossed. Find the probability of getting exactly 2 heads.
18. A bag contains 5 red, 4 green, and 3 blue balls. One ball is drawn at random. Find the probability it is red or green.
19. Two dice are thrown. Find the probability that the product of the numbers is even.
20. If \(A\) and \(B\) are independent events with \(P(A) = 0.6\) and \(P(B) = 0.5\), find \(P(A \cup B)\).
21. A card is drawn from a deck. Find the probability it is an ace or a face card.
22. A die is rolled. Find the probability of getting a number greater than 4.
23. Two coins are tossed. Find the probability of getting the same face.
24. A box contains 3 red, 2 green, and 5 blue balls. Two balls are drawn without replacement. Find the probability both are red.
25. In a class of 30 students, 18 like mathematics, 15 like physics, and 10 like both. Find the probability that a student likes mathematics or physics.
26. A die is rolled twice. Find the probability that the sum is a multiple of 3.
27. A card is drawn from a pack of 52 cards. Find the probability it is neither a red card nor a king.
28. A bag contains 6 white and 4 black balls. Two balls are drawn with replacement. Find the probability at least one is white.
29. A coin is tossed three times. Find the probability of getting at least one tail.
30. Two dice are thrown. Find the probability that the sum is greater than 10.
31. A box contains 5 red and 3 blue balls. Three balls are drawn at random. Find the probability of exactly two red balls.
32. A die is rolled twice. Find the probability of getting one odd and one even number.
33. If \(P(A) = 0.7\) and \(P(B) = 0.4\) and \(P(A \cap B) = 0.2\), find \(P(A|B)\).
34. A bag contains 3 red and 2 green balls. Two balls are drawn without replacement. Find the probability they are of different colors.
35. A die is rolled. Find the probability that the number is less than 5.
36. A card is drawn from a pack. Find the probability it is a face card given that it is a black card.
37. Two dice are thrown. Find the probability that the sum is 9 or 11.
38. A box contains 8 balls, 5 red and 3 green. One ball is drawn at random. Find the probability it is not red.
39. A family has 3 children. Find the probability that at least one child is a boy.
40. In a deck of cards, find the probability of drawing a red card given that it is a face card.

Part B: Random Variables & Distributions (Q41–80)

Here we explore discrete and continuous random variables. Learn to calculate expected values, variance, and probabilities using binomial, Poisson, and normal distributions.

41. Define a random variable with an example.
42. The probability distribution of a discrete random variable \(X\) is given by:

    | X   | 0   | 1   | 2   | 3   |
    |-----|-----|-----|-----|-----|
    | P(X)| 0.1 | 0.2 | 0.4 | 0.3 |
    

    Find \(E(X)\).
43. A binomial distribution has \(n = 5\), \(p = 0.6\). Find \(P(X = 3)\).
44. In a Poisson distribution, the mean \(\lambda = 4\). Find \(P(X = 2)\).
45. \(X \sim N(50, 25)\). Find \(P(45 < X < 55)\).
46. Binomial distribution with \(n = 10\), \(p = 0.2\). Find variance.
47. A discrete random variable has:

    | X   | 1   | 2   | 3   |
    |-----|-----|-----|-----|
    | P(X)| 0.2 | 0.5 | 0.3 |
    

    Find \(E(X^2)\).
48. A Poisson variable has variance 5. Find the mean.
49. A normal variable has \(\mu = 100\), \(\sigma = 15\). Find \(P(X > 130)\).
50. A binomial variable has \(n = 8\), \(p = 0.3\). Find \(P(X \le 2)\).
51. If \(X\) has a binomial distribution with \(n = 4\), \(p = 0.5\), find \(P(X \ge 3)\).
52. \(X \sim Poisson(3)\). Find \(P(X \le 2)\).
53. \(X \sim N(0,1)\). Find \(P(-1 < X < 1)\).
54. If \(X \sim Binomial(n, p)\) and \(E(X) = 4\), \(\text{Var}(X) = 2\), find \(n\) and \(p\).
55. A discrete variable has \(X = 0,1,2,3,4\) with \(P(X) = k, 2k, 3k, 4k\). Find \(k\).
56. \(X \sim Binomial(5, 0.6)\). Find \(P(X = 0)\).
57. \(X \sim Poisson(2)\). Find \(P(X \ge 3)\).
58. \(X \sim N(20,4)\). Find \(P(X < 18)\).
59. A random variable \(X\) takes values 0,1,2,3,4 with equal probability. Find \(E(X)\).
60. \(X \sim Binomial(10,0.5)\). Find \(P(4 \le X \le 6)\).
61. \(X \sim Poisson(6)\). Find \(P(X=6)\).
62. \(X \sim N(100,25)\). Find \(P(90 < X < 110)\).
63. Find \(E(X)\) if \(X \sim Binomial(n=5, p=0.3)\).
64. If \(X \sim Poisson(\lambda=3)\), find \(P(X\neq 2)\).
65. \(X \sim N(50,16)\). Find \(P(X>54)\).
66. A discrete variable \(X\) has \(P(X=0)=0.1\), \(P(X=1)=0.2\), \(P(X=2)=0.3\), \(P(X=3)=0.4\). Find variance.
67. \(X \sim Binomial(6,0.4)\). Find \(P(X<3 li="">
68. \(X \sim Poisson(5)\). Find \(P(X \le 4)\).
69. \(X \sim N(60,36)\). Find \(P(54 < X < 66)\).
70. \(X \sim Binomial(8,0.7)\). Find \(P(X=5)\).
71. A discrete variable has distribution:

    | X | 0 | 1 | 2 | 3 | 4 |
    |---|---|---|---|---|---|
    | P | 0.1 | 0.2 | 0.2 | 0.3 | 0.2 |
    

    Find \(E(X)\).
72. \(X \sim Poisson(2)\). Find \(P(X=0 \text{ or } X=1)\).
73. \(X \sim N(80,16)\). Find \(P(X \le 78)\).
74. \(X \sim Binomial(5,0.5)\). Find \(P(X \ge 4)\).
75. \(X \sim Poisson(3)\). Find \(P(X \le 1)\).
76. \(X \sim N(0,1)\). Find \(P(X < -1.5)\).
77. Find \(Var(X)\) if \(X \sim Binomial(10,0.6)\).
78. \(X \sim Poisson(4)\). Find \(P(X \ge 2)\).
79. \(X \sim N(100,49)\). Find \(P(90 < X < 110)\).
80. \(X \sim Binomial(7,0.3)\). Find \(P(3 \le X \le 5)\).

Part C: Mixed Applications & Higher-order Questions (Q81–120)

This section challenges you with application-based and higher-order probability problems, combining multiple concepts and real-world scenarios.

81. Two dice are rolled. Find the probability that the sum is divisible by 3.
82. Three coins are tossed. Find the probability of getting at least 2 heads.
83. A bag contains 5 red, 6 green, and 4 blue balls. Two balls are drawn randomly. Find probability they are of different colors.
84. A die is rolled three times. Find the probability of getting at least one 6.
85. A family has 4 children. Find the probability of having exactly 2 girls.
86. A box contains 10 balls numbered 1–10. One ball is drawn at random. Find probability the number is prime or even.
87. Two dice are thrown. Find the probability that the sum is a perfect square.
88. Three coins are tossed. Find the probability of all heads or all tails.
89. In a class of 50 students, 20 play football, 25 play cricket, and 10 play both. Find the probability that a randomly selected student plays football or cricket.
90. A bag contains 4 white and 6 black balls. Two balls are drawn with replacement. Find the probability both are white.
91. A die is rolled twice. Find the probability that the sum is a prime number.
92. A card is drawn. Find the probability it is a red card or a queen.
93. Two coins are tossed. Find the probability that both show the same face.
94. A box contains 3 red, 4 blue, and 5 green balls. One ball is drawn at random. Find the probability it is blue or green.
95. Two dice are thrown. Find the probability that one shows 5 and the other shows 6.
96. A bag contains 2 red, 3 green, and 5 blue balls. Two balls are drawn without replacement. Find probability they are same color.
97. Three dice are rolled. Find the probability of getting a sum of 10.
98. A family has 3 children. Find the probability of having exactly 1 boy.
99. A die is rolled four times. Find the probability of getting exactly two 6’s.
100. A bag contains 5 white and 3 black balls. Two balls are drawn with replacement. Find the probability of at least one black.
101. A binomial variable has \(n=5\), \(p=0.4\). Find \(P(X=2)\).
102. \(X \sim Poisson(3)\). Find \(P(X \le 2)\).
103. \(X \sim N(50,9)\). Find \(P(47 < X < 53)\).
104. Two dice are thrown. Find the probability that the sum is greater than 9.
105. A card is drawn from a deck. Find probability it is a king given that it is a face card.
106. A box contains 10 balls numbered 1–10. Two balls are drawn. Find probability sum is odd.
107. Three coins are tossed. Find the probability of exactly one head.
108. A bag contains 3 red and 2 green balls. Two balls drawn without replacement. Find probability first red then green.
109. A die is rolled twice. Find probability both numbers are odd.
110. A family has 2 children. Find probability both are of same gender.
111. A die is rolled thrice. Find probability all numbers are distinct.
112. A card is drawn. Find probability it is neither king nor queen.
113. Two dice are thrown. Find probability that the difference of numbers is 1.
114. Three coins tossed. Probability of at least one head.
115. A bag has 6 white and 4 black balls. Two drawn with replacement. Probability of different colors.
116. A binomial variable \(X\) has \(n=6\), \(p=0.5\). Find \(P(X\ge4)\).
117. \(X \sim Poisson(4)\). Find \(P(X=3 \text{ or } X=4)\).
118. \(X \sim N(100,16)\). Find \(P(96 < X < 104)\).
119. A discrete variable \(X\) has \(P(X=1)=0.2\), \(P(X=2)=0.5\), \(P(X=3)=0.3\). Find \(E(X)\).
120. Two dice rolled. Find probability sum is neither 7 nor 11.

Answers

Click to View Answers

1. 4/6 = 2/3
2. 3/4
3. 6/52 = 3/26
4. 6/36 = 1/6
5. 5/8
6. 6/36 = 1/6
7. 2/15
8. 1/4
9. 3/10
10. Max = 0.4, Min = 0.1
11. 16/52 = 4/13
12. 49/100
13. 6/36 = 1/6
14. 11/36
15. 7/10
16. 15/30 = 1/2
17. 3/8
18. 9/12 = 3/4
19. 3/4
20. 0.8
21. 16/52 = 4/13
22. 2/6 = 1/3
23. 1/2
24. 3/10
25. 3/15 = 1/5
26. 23/30
27. 6/36 = 1/6
28. 36/52 = 9/13
29. 9/16
30. 0.5
31. 1/2
32. 120/216 = 5/9
33. 12/13
34. 5/18
35. 7/8
36. 0.9
37. 0.3438
38. 0.4335
39. 0.6826
40. 2.1
41. 13/18
42. 2.5
43. 0.406
44. 0.346
45. 0.195
46. 0.6826
47. 2.0
48. 3.0
49. 5
50. 0.0668
51. 0.815
52. 0.6826
53. 0.275
54. Var = 2
55. k = 0.1
56. 0.07776
57. 0.1991
58. 0.081
59. 0.3087
60. 2.0
61. 0.6826
62. 0.3438
63. 0.4335
64. 0.6826
65. 0.875
66. 2.0
67. 0.234
68. 0.2304
69. 0.857
70. 0.6826
71. 0.185
72. 0.815
73. 0.6826
74. 2.4
75. 0.406
76. 0.4207
77. 0.1875
78. 0.1991
79. 0.0668
80. 2.4
81. 0.815
82. 0.6826
83. 0.275
84. 1/3
85. 1/2
86. 0.74
87. 91/216
88. 3/8
89. 7/10
90. 1/6
91. 1/2
92. 7/10
93. 4/25
94. 5/12
95. 27/52
96. 1/2
97. 3/4
98. 1/18
99. 0.18
100. 1/8
101. 3/8
102. 25/1296
103. 55/64
104. 0.2304
105. 0.857
106. 0.6826
107. 1/6
108. 1/4
109. 1/2
110. 1/2
111. 3/8
112. 3/10
113. 1/4
114. 1/2
115. 5/9
116. 12/13
117. 5/18
118. 7/8
119. 0.9
120. 0.3438
121. 0.4335
122. 0.6826
123. 2.1
124. 13/18