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Mathematics - Probability

Practise 244 JEE Main previous year questions on Probability, compiled from papers spanning 2002 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 JEE Main tests.

Probability has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 244 questions in all. 20% of them were easy, 58% moderate and 21% tough. Most of its questions came from 2021, with 32 questions that year. In the last three years (2024–2026) it had 55 questions across 49 papers, about 1.1 per paper.

The chapter's 9 topics are not weighted equally: Classical Definition of Probability (78 questions, 32%), Conditional Probability and Multiplication Theorem (39 questions, 16%), and Random Variable and its Probability Distribution (39 questions, 16%) have been asked the most. Classical Definition of Probability has also led over the last five years, with 39 questions. Classical Definition of Probability has produced the most tough questions (23).

  1. 1A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the ent08 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  2. 2A bag contains coins fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of gett06 Apr, 2026 (M)Total Probability
  3. 3A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each draw06 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  4. 4A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. 05 Apr, 2026 (M)Baye's Theorem
  5. 5The probabilities that players and of a team are selected for the captaincy for a tournament are and , respectively. If is selected the capt05 Apr, 2026 (E)Total Probability
  6. 6A coin is tossed times. If the probability that exactly heads appear in the first six tosses and exactly heads appear in the last five tosse04 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  7. 7From a month of days, different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to , wh04 Apr, 2026 (E)Classical Definition of Probability
  8. 8A man throws a fair coin repeatedly. He gets points for each head he throws and points for each tail he throws. If the probability that he g02 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  9. 9A bag contains 10 balls out of which are red and ( ) are black, where . If three balls are drawn at random without replacement and all of th28 Jan, 2026 (M)Baye's Theorem
  10. 10The probability distribution of a random variable is given below : \( {array}{|c|c|c|c|c|c|c|c|c|} X & 4k & {30}{7}k & {32}{7}k & {34}{7}k &28 Jan, 2026 (E)Random Variable and its Probability Distribution
  11. 11From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of get24 Jan, 2026 (M)Bernoulli Trial and Binomial Distribution
  12. 12Let S be a set of 5 elements and denote the power set of S. Let E be an event of choosing an ordered pair ( ) from the set such that . If th24 Jan, 2026 (E)Classical Definition of Probability
  13. 13From the first 100 natural numbers, two numbers first and then are selected randomly without replacement. If the probability that is , then 23 Jan, 2026 (M)Classical Definition of Probability
  14. 14Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and 23 Jan, 2026 (E)Total Probability
  15. 15If a random variable has the probability distribution then is equal to22 Jan, 2026 (M)Random Variable and its Probability Distribution
  16. 16Two distinct numbers and are selected at random from . The probability, that their product is divisible by 3, is22 Jan, 2026 (M)Classical Definition of Probability
  17. 17A random variable takes values with probabilities respectively, where . Let and respectively be the mean and standard deviation of X such th21 Jan, 2026 (E)Random Variable and its Probability Distribution
  18. 18If and are two events such that , and , where denotes the complement of , then is equal:-08 Apr, 2025 (E)Classical Definition of Probability
  19. 19A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probabil07 Apr, 2025 (E)Conditional Probability and Multiplication Theorem
  20. 20Let a random variable X take values with and . Then the value of is :07 Apr, 2025 (E)Random Variable and its Probability Distribution
  21. 21The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at leas04 Apr, 2025 (M)Classical Definition of Probability
  22. 22A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let denote the number of defective pens. Then the04 Apr, 2025 (M)Random Variable and its Probability Distribution
  23. 23A card from a pack of 52 cards is lost. From the remaining 51 cards, cards are drawn and are found to be spades. If the probability of the l04 Apr, 2025 (E)Conditional Probability and Multiplication Theorem
  24. 24All five letter words are made using all the letters and arranged as in an English dictionary with serial numbers. Let the word at serial nu03 Apr, 2025 (M)Classical Definition of Probability
  25. 25If the probability that the random variable X takes the value is given by , , where k is a constant, then is equal to03 Apr, 2025 (E)Random Variable and its Probability Distribution
  26. 26Three distinct numbers are selected randomly from the set . If the probability, that the selected numbers are in an increasing G.P. is , , t02 Apr, 2025 (M)Classical Definition of Probability
  27. 27Given three indentical bags each containing 10 balls, whose colours are as follows : A person chooses a bag at random and takes out a ball. 02 Apr, 2025 (E)Conditional Probability and Multiplication Theorem
  28. 28Let be a matrix such that for all and . Let the random variable X denote the possible values of the determinant of the matrix . Then, the va29 Jan, 2025 (E)Random Variable and its Probability Distribution
  29. 29Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains white balls and 3 black balls. One ball is drawn randomly from Bag 1 and 29 Jan, 2025 (E)Total Probability
  30. 30Two number and are randomly chosen from the set of natural numbers. Then, the probability that the value of is non-zero, equals28 Jan, 2025 (M)Classical Definition of Probability
  31. 31Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. 28 Jan, 2025 (M)Random Variable and its Probability Distribution
  32. 32Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected a28 Jan, 2025 (E)Classical Definition of Probability
  33. 33Bag contains 6 white and 4 blue balls, Bag contains 4 white and 6 blue balls, and Bag contains 5 white and 5 blue balls. One of the bags is 28 Jan, 2025 (E)Baye's Theorem
  34. 34and alternately throw a pair of dice. wins if he throws a sum of 5 before throws a sum of 8 , and wins if he throws a sum of 8 before throws24 Jan, 2025 (M)Classical Definition of Probability
  35. 35Let be a square matrix of order 2 with entries either 0 or 1 . Let be the event that is an invertible matrix. Then the probability is :24 Jan, 2025 (E)Classical Definition of Probability
  36. 36One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two face23 Jan, 2025 (M)Classical Definition of Probability
  37. 37A board has 16 squares as shown in the figure: Out of these 16 squares, two squares are chosen at random. The probability that they have no 23 Jan, 2025 (E)Classical Definition of Probability
  38. 38Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the22 Jan, 2025 (M)Baye's Theorem
  39. 39A coin is tossed three times. Let denote the number of times a tail follows a head. If and denote the mean and variance of , then the value 22 Jan, 2025 (M)Random Variable and its Probability Distribution
  40. 40If and are two events such that , and and are the roots of the equation , then the value of is :22 Jan, 2025 (E)Conditional Probability and Multiplication Theorem
  41. 41Let and denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked . If the probability that has a09 Apr, 2024 (M)Classical Definition of Probability
  42. 42If an unbiased dice is rolled thrice, then the probability of getting a greater number in the roll than the number obtained in the roll, , i09 Apr, 2024 (E)Classical Definition of Probability
  43. 43Let the sum of two positive integers be 24 . If the probability, that their product is not less than times their greatest possible product, 08 Apr, 2024 (M)Addition and Subtraction Theorems
  44. 44Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables and respectively denote the number08 Apr, 2024 (M)Random Variable and its Probability Distribution
  45. 45There are three bags and . Bag contains 5 one-rupee coins and 4 five-rupee coins; Bag contains 4 one-rupee coins and 5 five-rupee coins and 08 Apr, 2024 (E)Baye's Theorem
  46. 46A company has two plants and to manufacture motorcycles. motorcycles are manufactured at plant and the remaining are manufactured at plant o06 Apr, 2024 (M)Baye's Theorem
  47. 47If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly tw06 Apr, 2024 (E)Classical Definition of Probability
  48. 48From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable denote the number of defecti06 Apr, 2024 (E)Random Variable and its Probability Distribution
  49. 49The coefficients in the quadratic equation are chosen from the set . The probability of this equation having repeated roots is :05 Apr, 2024 (M)Classical Definition of Probability
  50. 50The coefficients in the quadratic equation are from the set . If the probability of this equation having one real root bigger than the other05 Apr, 2024 (E)Classical Definition of Probability

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 244 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

3.Is Probability an important chapter for JEE Main Mathematics?

Probability has appeared in 25 of the 25 years of JEE Main papers covered here, with 244 questions across 192 papers - about one per paper it appears in.

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

Of the 244 questions analysed for this chapter, 20% are easy, 58% moderate and 21% tough. 2021 had the most, with 32 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 78 questions (32%)
  • Conditional Probability and Multiplication Theorem - 39 questions (16%)
  • Random Variable and its Probability Distribution - 39 questions (16%)
  • Classical Definition of Probability has produced the most tough questions (23).
6.Is Probability's weightage in JEE Main going up or down?

Across all 192 papers analysed, Probability has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.1 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.