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Chapter 16: Probability

NCERT Solutions for CBSE Class 10 Mathematics — 91 solved questions with detailed explanations.

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Solved Questions

Q1. A card is drawn from a standard deck of 52 cards. The probability of getting a face card is:

3/13
1/4
4/13
1/13

Difficulty: Easy · Topic: Cards

Solution

Face cards: J, Q, K = 12 cards. P = 12/52 = 3/13.

Q2. Two dice are thrown. The probability of getting a sum of 7 is:

1/6
5/36
7/36
1/12

Difficulty: Easy-Medium · Topic: Dice

Solution

Favorable outcomes: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6. P = 6/36 = 1/6.

Q3. If P(A) = 0.4, P(B) = 0.3, and A and B are independent, then P(A ∩ B) is:

0.12
0.70
0.10
0.42

Difficulty: Easy-Medium · Topic: Independent Events

Solution

For independent events: P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.

Q4. P(A∪B) = P(A)+P(B)-P(A∩B) is the

addition theorem
Bayes theorem
multiplication theorem
complement rule

Difficulty: Easy-Medium · Topic: Probability

Solution

addition theorem.

Q5. For mutually exclusive events, P(A∩B) =

P(A)×P(B)
1
0
P(A)+P(B)

Difficulty: Easy-Medium · Topic: Probability

Solution

0.

Q6. P(A') = 1-P(A) is the

complement rule
addition rule
Bayes rule
multiplication rule

Difficulty: Easy-Medium · Topic: Probability

Solution

complement rule.

Q7. P(A)=0.1, P(B)=0.1, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.1=1.0.

Q8. P(A)=0.1, P(B)=0.2, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.2=0.5.

Q9. P(A)=0.1, P(B)=0.3, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.3=0.3333.

Q10. P(A)=0.1, P(B)=0.4, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.4=0.25.

Q11. P(A)=0.1, P(B)=0.5, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.5=0.2.

Q12. P(A)=0.1, P(B)=0.6, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.6=0.1667.

Q13. P(A)=0.1, P(B)=0.7, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.7=0.1429.

Q14. P(A)=0.1, P(B)=0.8, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.8=0.125.

Q15. P(A)=0.1, P(B)=0.9, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.9=0.1111.

Q16. P(A)=0.2, P(B)=0.1, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.1=1.0.

Q17. P(A)=0.2, P(B)=0.2, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.2=0.5.

Q18. P(A)=0.2, P(B)=0.2, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.2=1.0.

Q19. P(A)=0.2, P(B)=0.3, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.3=0.3333.

Q20. P(A)=0.2, P(B)=0.3, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.3=0.6667.

Q21. P(A)=0.2, P(B)=0.4, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.4=0.25.

Q22. P(A)=0.2, P(B)=0.4, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.4=0.5.

Q23. P(A)=0.2, P(B)=0.5, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.5=0.2.

Q24. P(A)=0.2, P(B)=0.5, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.5=0.4.

Q25. P(A)=0.2, P(B)=0.6, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.6=0.1667.

Q26. P(A)=0.2, P(B)=0.6, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.6=0.3333.

Q27. P(A)=0.2, P(B)=0.7, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.7=0.1429.

Q28. P(A)=0.2, P(B)=0.7, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.7=0.2857.

Q29. P(A)=0.2, P(B)=0.8, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.8=0.125.

Q30. P(A)=0.2, P(B)=0.8, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.8=0.25.

Q31. P(A)=0.2, P(B)=0.9, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.9=0.1111.

Q32. P(A)=0.2, P(B)=0.9, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.9=0.2222.

Q33. P(A)=0.3, P(B)=0.1, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.1=1.0.

Q34. P(A)=0.3, P(B)=0.2, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.2=0.5.

Q35. P(A)=0.3, P(B)=0.2, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.2=1.0.

Q36. P(A)=0.3, P(B)=0.3, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.3=0.3333.

Q37. P(A)=0.3, P(B)=0.3, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.3=0.6667.

Q38. P(A)=0.3, P(B)=0.3, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.3=1.0.

Q39. P(A)=0.3, P(B)=0.4, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.4=0.25.

Q40. P(A)=0.3, P(B)=0.4, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.4=0.5.

Q41. P(A)=0.3, P(B)=0.4, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.4=0.75.

Q42. P(A)=0.3, P(B)=0.5, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.5=0.2.

Q43. P(A)=0.3, P(B)=0.5, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.5=0.4.

Q44. P(A)=0.3, P(B)=0.5, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.5=0.6.

Q45. P(A)=0.3, P(B)=0.6, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.6=0.1667.

Q46. P(A)=0.3, P(B)=0.6, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.6=0.3333.

Q47. P(A)=0.3, P(B)=0.6, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.6=0.5.

Q48. P(A)=0.3, P(B)=0.7, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.7=0.1429.

Q49. P(A)=0.3, P(B)=0.7, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.7=0.2857.

Q50. P(A)=0.3, P(B)=0.7, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.7=0.4286.

Q51. P(A)=0.3, P(B)=0.8, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.8=0.125.

Q52. P(A)=0.3, P(B)=0.8, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.8=0.25.

Q53. P(A)=0.3, P(B)=0.8, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.8=0.375.

Q54. P(A)=0.3, P(B)=0.9, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.9=0.1111.

Q55. P(A)=0.3, P(B)=0.9, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.9=0.2222.

Q56. P(A)=0.3, P(B)=0.9, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.9=0.3333.

Q57. P(A)=0.4, P(B)=0.1, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.1=1.0.

Q58. P(A)=0.4, P(B)=0.2, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.2=0.5.

Q59. P(A)=0.4, P(B)=0.2, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.2=1.0.

Q60. P(A)=0.4, P(B)=0.3, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.3=0.3333.

Q61. P(A)=0.4, P(B)=0.3, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.3=0.6667.

Q62. P(A)=0.4, P(B)=0.3, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.3=1.0.

Q63. P(A)=0.4, P(B)=0.4, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.4=0.25.

Q64. P(A)=0.4, P(B)=0.4, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.4=0.5.

Q65. P(A)=0.4, P(B)=0.4, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.4=0.75.

Q66. P(A)=0.4, P(B)=0.4, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.4=1.0.

Q67. P(A)=0.4, P(B)=0.5, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.5=0.2.

Q68. P(A)=0.4, P(B)=0.5, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.5=0.4.

Q69. P(A)=0.4, P(B)=0.5, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.5=0.6.

Q70. P(A)=0.4, P(B)=0.5, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.5=0.8.

Q71. P(A)=0.4, P(B)=0.6, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.6=0.1667.

Q72. P(A)=0.4, P(B)=0.6, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.6=0.3333.

Q73. P(A)=0.4, P(B)=0.6, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.6=0.5.

Q74. P(A)=0.4, P(B)=0.6, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.6=0.6667.

Q75. P(A)=0.4, P(B)=0.7, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.7=0.1429.

Q76. P(A)=0.4, P(B)=0.7, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.7=0.2857.

Q77. P(A)=0.4, P(B)=0.7, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.7=0.4286.

Q78. P(A)=0.4, P(B)=0.7, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.7=0.5714.

Q79. P(A)=0.4, P(B)=0.8, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.8=0.125.

Q80. P(A)=0.4, P(B)=0.8, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.8=0.25.

Q81. P(A)=0.4, P(B)=0.8, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.8=0.375.

Q82. P(A)=0.4, P(B)=0.8, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.8=0.5.

Q83. P(A)=0.4, P(B)=0.9, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.9=0.1111.

Q84. P(A)=0.4, P(B)=0.9, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.9=0.2222.

Q85. P(A)=0.4, P(B)=0.9, P(A∩B)=0.3. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.3/0.9=0.3333.

Q86. P(A)=0.4, P(B)=0.9, P(A∩B)=0.4. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.4/0.9=0.4444.

Q87. P(A)=0.5, P(B)=0.1, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.1=1.0.

Q88. P(A)=0.5, P(B)=0.2, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.2=0.5.

Q89. P(A)=0.5, P(B)=0.2, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.2=1.0.

Q90. P(A)=0.5, P(B)=0.3, P(A∩B)=0.1. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.1/0.3=0.3333.

Q91. P(A)=0.5, P(B)=0.3, P(A∩B)=0.2. P(A|B)=

Difficulty: Easy-Medium · Topic: Conditional

Solution

P(A|B)=P(A∩B)/P(B)=0.2/0.3=0.6667.

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics

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