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Mathematics - Probability

Practise 55 JEE Advanced previous year questions on Probability, compiled from papers spanning 2006 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 Advanced tests.

Probability has been asked in 21 of the 27 years of JEE Advanced papers analysed (2000–2026), with 55 questions in all. 13% of them were easy, 58% moderate and 29% tough. Most of its questions came from 2021, with 5 questions that year. In the last three years (2024–2026) it had 5 questions across 6 papers, about 0.8 per paper.

The chapter's 7 topics are not weighted equally: Conditional Probability and Multiplication Theorem (23 questions, 42%), Classical Definition of Probability (12 questions, 22%), and Baye's Theorem (8 questions, 15%) have been asked the most. Conditional Probability and Multiplication Theorem has also led over the last five years, with 4 questions. Independent Events has produced the most tough questions (5).

  1. 1Suppose that Box I contains red balls and green balls, and Box II contains red balls and green balls. All the balls of Box I and Box II are 2026 (Paper 1)Conditional Probability and Multiplication Theorem
  2. 2Three students and are given a problem to solve. Consider the following events : At least one of and can solve the problem, can solve the pr2025 (Paper 1)Conditional Probability and Multiplication Theorem
  3. 3A factory has a total of three manufacturing units, , and , which produce bulbs independent of each other. The units , and produce bulbs in 2025 (Paper 2)Baye's Theorem
  4. 4A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of so2024 (Paper 1)Baye's Theorem
  5. 5A bag contains balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identica2024 (Paper 2)Conditional Probability and Multiplication Theorem
  6. 6Let X = x , y : x 2 8 + y 2 20 1 and y 2 5 x . Three distinct point P , Q and R are randomly chosen from X . Then the probability that P , Q2023 (Paper 1)Classical Definition of Probability
  7. 7Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random to2023 (Paper 2)Classical Definition of Probability
  8. 8Consider the 6 6 square in the figure. Let A 1 , A 2 , , A 49 be the points of intersections (dots in the picture) in some order. We say tha2023 (Paper 2)Random Variable and its Probability Distribution
  9. 9Two players, P 1 and P 2 , play a game against each other. In every round of the game, each player rolls a fair die once, where the six face2022 (Paper 1)Conditional Probability and Multiplication Theorem
  10. 10Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-ll contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 2022 (Paper 2)Baye's Theorem
  11. 11Consider three sets E 1 = { 1 , 2 , 3 } , F 1 = { 1 , 3 , 4 } and G 1 = { 2 , 3 , 4 , 5 } . Two elements are chosen at random, without repla2021 (Paper 1)Conditional Probability and Multiplication Theorem
  12. 12Three numbers are chosen at random, one after another with replacement, from the set . Let be the probability that the maximum of chosen num2021 (Paper 1)Conditional Probability and Multiplication Theorem
  13. 13Three numbers are chosen at random, one after another with replacement, from the set . Let be the probability that the maximum of chosen num2021 (Paper 1)Conditional Probability and Multiplication Theorem
  14. 14Let E , F and G be three events having probabilities P ( E ) = 1 8 , P ( F ) = 1 6 and P ( G ) = 1 4 , and let P ( E F G ) = 1 10 For any ev2021 (Paper 1)Classical Definition of Probability
  15. 15A number is chosen at random from the set 1 , 2 , 3 , , 2000 . Let p be the probability that the chosen number is a multiple of 3 or 7 . The2021 (Paper 2)Classical Definition of Probability
  16. 16Let C 1 and C 2 be two biased coins such that the probabilities of getting head in a single toss are 2 3 and 1 3 , respectively. Suppose is 2020 (Paper 1)Conditional Probability and Multiplication Theorem
  17. 17The probability that a missile hits a target successfully is 0 . 75 . In order to destroy the target completely, at least three successful h2020 (Paper 2)Bernoulli Trial and Binomial Distribution
  18. 18Two fair dice, each with faces numbered 1 , 2 , 3 , 4 , 5 and 6 , are rolled together and the sum of the numbers on the faces is observed. T2020 (Paper 2)Conditional Probability and Multiplication Theorem
  19. 19There are three bags B 1 , B 2 and B 3 . The bag B 1 contains 5 red and 5 green balls, B 2 contains 3 red and 5 green balls, and B 3 contain2019 (Paper 1)Conditional Probability and Multiplication Theorem
  20. 20Let S be the sample space of all 3 3 matrices with entries from the set 0 , 1 . Let the events E 1 and E 2 be given by E 1 = A S : d e t A =2019 (Paper 1)Conditional Probability and Multiplication Theorem
  21. 21Let X denote the number of elements in set X . Let S = 1 , 2 , 3 , 4 , 5 , 6 be a sample space, where each element is equally likely to occu2019 (Paper 2)Independent Events
  22. 22Paragraph: There are five students S 1 , S 2 , S 3 , S 4 and S 5 in a music class and for them there are five seats R 1 , R 2 , R 3 , R 4 an2018 (Paper 1)Classical Definition of Probability
  23. 23Paragraph: There are five students S 1 , S 2 , S 3 , S 4 and S 5 in a music class and for them there are five seats R 1 , R 2 , R 3 , R 4 an2018 (Paper 1)Classical Definition of Probability
  24. 24Let X and Y be two events such that P X = 1 3 , P X Y = 1 2 and P Y | X = 2 5 . Then2017 (Paper 1)Conditional Probability and Multiplication Theorem
  25. 25Three randomly chosen non negative integers x , y , z are found to satisfy the equation x + y + z = 10 . Then the probability that z is even2017 (Paper 2)Classical Definition of Probability
  26. 26A computer producing factory has only two plants T 1 and T 2 . Plant T 1 produces 20 % and plant T 2 produces 80 % of the total computers pr2016 (Paper 1)Baye's Theorem
  27. 27Paragraph: Football teams and have to play two games against each other. It is assumed that the outcomes of the two games are independent. T2016 (Paper 2)Conditional Probability and Multiplication Theorem
  28. 28Paragraph: Football teams and have to play two games against each other. It is assumed that the outcomes of the two games are independent. T2016 (Paper 2)Conditional Probability and Multiplication Theorem
  29. 29The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least 0 . 96 , is2015 (Paper 1)Bernoulli Trial and Binomial Distribution
  30. 30Let n 1 a n d n 2 be the number of red and black balls, respectively, in box I. Let n 3 a n d n 4 be the number of red and black balls, resp2015 (Paper 2)Baye's Theorem
  31. 31Let n 1 a n d n 2 be the number of red and black balls, respectively, in box I. Let n 3 a n d n 4 be the number of red and black balls, resp2015 (Paper 2)Conditional Probability and Multiplication Theorem
  32. 32Paragraph: Box contains three cards bearing numbers ; box contains five cards bearing numbers ; and box contains seven cards bearing numbers2014 (Paper 2)Classical Definition of Probability
  33. 33Four persons independently solve a certain problem correctly with probabilities 1 2 , 3 4 , 1 4 , 1 8 . Then the probability that the proble2013 (Paper 1)Addition and Subtraction Theorems
  34. 34Of the three independent events E 1 , E 2 and E 3 , the probability that only E 1 occurs is , only E 2 occurs is and only E 3 occurs is . Le2013 (Paper 1)Independent Events
  35. 35Paragraph: A box contains white ball, red balls and black balls. Another box contains white balls, red balls and black balls. A third box co2013 (Paper 2)Baye's Theorem
  36. 36Paragraph: A box contains white ball, red balls and black balls. Another box contains white balls, red balls and black balls. A third box co2013 (Paper 2)Baye's Theorem
  37. 37A ship is fitted with three engines and . The engines function independently of each other with respective probabilities and . For the ship 2012 (Paper 1)Independent Events
  38. 38Four fair dice and ; each having six faces numbered and 6 are rolled simultaneously. The probability that shows a number appearing on one of2012 (Paper 2)Bernoulli Trial and Binomial Distribution
  39. 39Let and be two events such that , and . Which of the following is (are) correct?2012 (Paper 2)Independent Events
  40. 40Paragraph: Let and be two urns such that contains 3 white and 2 red balls and contains only 1 white ball. A fair coin is tossed. If head app2011 (Paper 1)Conditional Probability and Multiplication Theorem
  41. 41Paragraph: Let and be two urns such that contains 3 white and 2 red balls and contains only 1 white ball. A fair coin is tossed. If head app2011 (Paper 1)Baye's Theorem
  42. 42Let and be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If 2011 (Paper 2)Addition and Subtraction Theorems
  43. 43Let be a complex cube root of unity with . A fair die is thrown three times. If and are the numbers obtained on the die, then the probabilit2010 (Paper 1)Classical Definition of Probability
  44. 44A signal which can be green or red with probability and respectively, is received by station and then transmitted to station B. The probabil2010 (Paper 2)Independent Events
  45. 45Paragraph: A fair die is tossed repeatedly until a six is obtained. Let denotes the number of tosses required. Question: The probability tha2009 (Paper 1)Classical Definition of Probability
  46. 46Paragraph: A fair die is tossed repeatedly until a six is obtained. Let denotes the number of tosses required. Question: The probability tha2009 (Paper 1)Classical Definition of Probability
  47. 47Paragraph: A fair die is tossed repeatedly until a six is obtained. Let denotes the number of tosses required. Question: The conditional pro2009 (Paper 1)Conditional Probability and Multiplication Theorem
  48. 48Consider the system of equations where Statement 1 The probability that the system of equations has a unique solution, is . Statement 2 The 2008 (Paper 1)Conditional Probability and Multiplication Theorem
  49. 49An experiment has 10 equally likely outcomes. Let and be two non-empty events of the experiment. If consists of 4 outcomes, the number of ou2008 (Paper 2)Independent Events
  50. 50One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that t2007 (Paper 1)Conditional Probability and Multiplication Theorem

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 55 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Probability has appeared in 21 of the 21 years of JEE Advanced papers covered here, with 55 questions across 37 papers - about one per paper it appears in.

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

Of the 55 questions analysed for this chapter, 13% are easy, 58% moderate and 29% tough. 2021 had the most, with 5 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Conditional Probability and Multiplication Theorem - 23 questions (42%)
  • Classical Definition of Probability - 12 questions (22%)
  • Baye's Theorem - 8 questions (15%)
  • Independent Events has produced the most tough questions (5).
6.Is Probability's weightage in JEE Advanced going up or down?

Across all 37 papers analysed, Probability has averaged about 1.5 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.