Jump to a section

Mathematics - Probability

Practise 290 NDA previous year questions on Probability, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Probability has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 290 questions in all. 23% of them were easy, 77% moderate and 0% tough. Most of its questions came from 2025, with 27 questions that year. In the last three years (2024–2026) it had 61 questions across 5 papers, about 12.2 per paper.

The chapter's 9 topics are not weighted equally: Classical Definition of Probability (111 questions, 38%), Addition and Subtraction Theorems (50 questions, 17%), and Bernoulli Trial and Binomial Distribution (37 questions, 13%) have been asked the most. Classical Definition of Probability has also led over the last five years, with 41 questions.

  1. 1Passage: A 4-digit number is selected at random formed by using the digits , , , and (where repetition of digits is not allowed). Question: 2026 (Phase 1)Classical Definition of Probability
  2. 2Passage: Let , , and be mutually exclusive and exhaustive events and . Question: What is equal to ?2026 (Phase 1)Addition and Subtraction Theorems
  3. 3Passage: Let , , and be mutually exclusive and exhaustive events and . Question: What is equal to ?2026 (Phase 1)Addition and Subtraction Theorems
  4. 4Passage: Let , , and be mutually exclusive and exhaustive events and . Question: If is the geometric mean of , , and , then what is equal to2026 (Phase 1)Classical Definition of Probability
  5. 5Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is ?2026 (Phase 1)Classical Definition of Probability
  6. 6Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is at least ?2026 (Phase 1)Classical Definition of Probability
  7. 7In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probabi2026 (Phase 1)Baye's Theorem
  8. 8Consider the following statements in respect of the events , , : I. is an impossible event. II. is a possible event. Which of the statements2026 (Phase 1)Classical Definition of Probability
  9. 9For a Binomial distribution with mean and standard deviation , what is the value of ?2026 (Phase 1)Bernoulli Trial and Binomial Distribution
  10. 10Three events , and are such that and are disjoint, and are independent, and are independent. If and , then what is the value of ?2026 (Phase 1)Addition and Subtraction Theorems
  11. 11Consider the following for the two (02) items that follow: Let be a random variable following binomial distribution with parameters and . Fu2025 (Phase 1)Bernoulli Trial and Binomial Distribution
  12. 12Consider the following for the two (02) items that follow: Let be a random variable following binomial distribution with parameters and . Fu2025 (Phase 1)Bernoulli Trial and Binomial Distribution
  13. 13Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What2025 (Phase 1)Classical Definition of Probability
  14. 14Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What2025 (Phase 1)Classical Definition of Probability
  15. 15Consider the following for the two (02) items that follow: The probabilities that , and become managers are , and respectively. The probabil2025 (Phase 1)Total Probability
  16. 16Consider the following for the two (02) items that follow: The probabilities that , and become managers are , and respectively. The probabil2025 (Phase 1)Baye's Theorem
  17. 17If , and , then what is the value of ?2025 (Phase 1)Conditional Probability and Multiplication Theorem
  18. 18If , and , then what is the value of ?2025 (Phase 1)Addition and Subtraction Theorems
  19. 19If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?2025 (Phase 1)Classical Definition of Probability
  20. 20The probability of a man hitting a target is . If the man fires 7 times, then what is the probability that he hits the target at least twice2025 (Phase 1)Bernoulli Trial and Binomial Distribution
  21. 21Let be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the numb2025 (Phase 1)Bernoulli Trial and Binomial Distribution
  22. 22In a sample survey of a village, the probability that a farmer is in debt is . What is the probability that three randomly selected farmers 2025 (Phase 2)Independent Events
  23. 23The probability that a family owns a laptop is ; that it also owns a desktop is . If the probability that it owns both is , then what is the2025 (Phase 2)Addition and Subtraction Theorems
  24. 24An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?2025 (Phase 2)Classical Definition of Probability
  25. 25An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and 2025 (Phase 2)Classical Definition of Probability
  26. 26Under which of the following conditions may binomial distribution be used? I. The number of trials is infinite and not fixed. II. The trials2025 (Phase 2)Bernoulli Trial and Binomial Distribution
  27. 27A person speaks the truth 4 out of 5 times and person speaks the truth 5 out of 6 times. What is the probability that they will contradict e2025 (Phase 2)Independent Events
  28. 28The probability that a student passes Physics test is and the probability that he passes both Physics test and English test is . The probabi2025 (Phase 2)Addition and Subtraction Theorems
  29. 29An event can happen with probability and event can happen with probability . Further, and are independent events. Which of the following sta2025 (Phase 2)Independent Events
  30. 30Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the col2025 (Phase 2)Classical Definition of Probability
  31. 31A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively?2025 (Phase 2)Classical Definition of Probability
  32. 32In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which is neither prime no2025 (Phase 2)Classical Definition of Probability
  33. 33An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible by 5 nor 9?2025 (Phase 2)Classical Definition of Probability
  34. 34Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?2025 (Phase 2)Classical Definition of Probability
  35. 35Let be a random variable following binomial distribution with parameters and . Further, and . What is the value of ?2025 (Phase 2)Bernoulli Trial and Binomial Distribution
  36. 36If , and , then what is the value of ?2025 (Phase 2)Conditional Probability and Multiplication Theorem
  37. 37If , and , then what is the value of ?2025 (Phase 2)Addition and Subtraction Theorems
  38. 38A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colo2024 (Phase 1)Classical Definition of Probability
  39. 39If a random variable follows binomial distribution with mean 5 and variance 4 , and , then what is the value of ?2024 (Phase 1)Bernoulli Trial and Binomial Distribution
  40. 40If two random variable X and Y are connected by relation and X follows Binomial distribution with parameters and , then what is the variance2024 (Phase 1)Random Variable and its Probability Distribution
  41. 41If the letters of the word "TIRUPATI" are written down at random, then what is the probability that both Ts are always consecutive?2024 (Phase 1)Classical Definition of Probability
  42. 42Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the num2024 (Phase 1)Classical Definition of Probability
  43. 43Let A and B be two events such that 0.75 and . What is the minimum value of ?2024 (Phase 1)Addition and Subtraction Theorems
  44. 44Let A and B be two events such that 0.75 and . What is the maximum value of ?2024 (Phase 1)Addition and Subtraction Theorems
  45. 45, and C are three events such that , and and . What is the minimum value of ?2024 (Phase 1)Addition and Subtraction Theorems
  46. 46, and C are three events such that , and and . What is the maximum value of ?2024 (Phase 1)Addition and Subtraction Theorems
  47. 47An unbiased coin is tossed times. The probability of getting at least one tail is and the probability of at What is the value of ?2024 (Phase 1)Total Probability
  48. 48An unbiased coin is tossed times. The probability of getting at least one tail is and the probability of at What is the value of ?2024 (Phase 1)Addition and Subtraction Theorems
  49. 49Three distinct natural numbers are chosen at random from 1 to 10 . What is the probability that they are consecutive?2024 (Phase 2)Classical Definition of Probability
  50. 50are three mutually exclusive and exhaustive events associated with a random experiment. If and , then what is equal to?2024 (Phase 2)Addition and Subtraction Theorems

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 290 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Probability chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Probability an important chapter for NDA Mathematics?

Probability has appeared in 17 of the 17 years of NDA papers covered here, with 290 questions across 32 papers - about 9 per paper it appears in.

4.What is the difficulty level of Probability questions in NDA?

Of the 290 questions analysed for this chapter, 23% are easy, 77% moderate and 0% tough. 2025 had the most, with 27 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 111 questions (38%)
  • Addition and Subtraction Theorems - 50 questions (17%)
  • Bernoulli Trial and Binomial Distribution - 37 questions (13%)
6.Is Probability's weightage in NDA going up or down?

Across all 32 papers analysed, Probability has averaged about 9.1 questions per paper. In the last three years (2024–2026), that average has risen, at about 12.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.