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Mathematics - Probability

Practise 50 WBJEE previous year questions on Probability, compiled from papers spanning 2009 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 WBJEE tests.

Probability has been asked in 18 of the 18 years of WBJEE papers analysed (2009–2026), with 50 questions in all. 36% of them were easy, 58% moderate and 6% tough. Most of its questions came from 2015, with 6 questions that year. In the last three years (2024–2026) it had 9 questions across 3 papers, about 3 per paper.

The chapter's 7 topics are not weighted equally: Classical Definition of Probability (20 questions, 40%), Addition and Subtraction Theorems (7 questions, 14%), and Conditional Probability and Multiplication Theorem (7 questions, 14%) have been asked the most. Classical Definition of Probability has also led over the last five years, with 7 questions. Classical Definition of Probability has produced the most tough questions (3).

  1. 1Consider the sequence of numbers . A person choose three numbers at random from the sequence. The probability that the chosen three number f2026Classical Definition of Probability
  2. 2Four natural numbers selected at random are multiplied together, then the probability that the digit in the unit's place in the product be 12026Classical Definition of Probability
  3. 3If be independent events such that and the probability that none of the events occurs be , then2026Independent Events
  4. 4If and are two independent events with and , then equals2025Independent Events
  5. 5The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is2025Classical Definition of Probability
  6. 6Three numbers are chosen at random without replacement from . The probability that the minimum of the chosen numbers is 3 or their maximum i2025Classical Definition of Probability
  7. 7Two smallest squares are chosen one by one on a chess board. The probability that they have a side in common is2024Classical Definition of Probability
  8. 8Two integers and are drawn one at a time without replacement from the set . Then2024Conditional Probability and Multiplication Theorem
  9. 9A biased coin with probability of getting head is tossed until a head appears for the first time. If the probability that the number of toss2024Bernoulli Trial and Binomial Distribution
  10. 10Let \(A\) and \(B\) are two independent events. The probability that both \(A\) and \(B\) happen is \( {1}{12}\) and probability that neithe2023Independent Events
  11. 11Let \(S\) be the sample space of the random experiment of throwing simultaneously two unbiased dice and \(E_k=\{a, b) \) \(S: a b=k\}\). If 2023Classical Definition of Probability
  12. 12A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinan2022Classical Definition of Probability
  13. 13are mutually exclusive events such that and . Then the set of possible values of are in2022Addition and Subtraction Theorems
  14. 14The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two succsses is2021Bernoulli Trial and Binomial Distribution
  15. 15Four persons and throw an unbiased die, turn by turn in succession till one gets an even number and win the game. What is the probability th2021Classical Definition of Probability
  16. 16Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the pro2020Conditional Probability and Multiplication Theorem
  17. 17A rifleman is firing at a distant target and has only chance of hitting it. The least number of rounds he must fire to have more than chance2020Bernoulli Trial and Binomial Distribution
  18. 18A and are independent events. The probability that both A and occur is and the probability that neither of them occurs is . The probability 2020Addition and Subtraction Theorems
  19. 19A problem in mathematics is given to 4 students whose chances of solving individually are and The probability that the problem will be solve2019Independent Events
  20. 20In order to get a head at least once with probability , the minimum number of times a unbiased coin needs to be tossed is2018Bernoulli Trial and Binomial Distribution
  21. 21student appears for tests 1 , 11 and . The student is successful if he passes in tests I,II or I, III. The probabilities of the student pass2018Addition and Subtraction Theorems
  22. 22The probability that a non-leap year selected at random will have 53 Sunday is2017Classical Definition of Probability
  23. 23Let and be two events such that and then2016Conditional Probability and Multiplication Theorem
  24. 24In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a selected a2016Conditional Probability and Multiplication Theorem
  25. 25If are two events such that and then2016Addition and Subtraction Theorems
  26. 26In a certain town, of the families own a car, own a house and own both car and house. If a family is randomly chosen. then what is the proba2015Addition and Subtraction Theorems
  27. 27A fair coin is tossed at a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 2015Bernoulli Trial and Binomial Distribution
  28. 28A person goes to office by car, scooter, bus and train, probability of which are . and respectively. Probability that he reaches office late2015Conditional Probability and Multiplication Theorem
  29. 29If 5 distinct balls are placed at random into 5 cells, then the probability that exactly one cell remains empty, is2015Classical Definition of Probability
  30. 30A survey of people in a given region showed that were smokers. The probability of death due to lung cancer given that a person smoked was 102015Conditional Probability and Multiplication Theorem
  31. 31Suppose a machine produces metal parts that contain some defective parts witl probability How many parts should be produced in order that th2015Bernoulli Trial and Binomial Distribution
  32. 32Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a b2014Total Probability
  33. 33A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to2014Classical Definition of Probability
  34. 34A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct2014Baye's Theorem
  35. 35A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then, the probability that a poker hand consists of 2014Classical Definition of Probability
  36. 36For two events and let and The necessarily false statement(s) is/are2014Classical Definition of Probability
  37. 37Each of and can take values 1 or 2 with equal probability. The probability that the equation has real roots, is equal to2013Classical Definition of Probability
  38. 38Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or2013Conditional Probability and Multiplication Theorem
  39. 39There are two coins, one unbiased with probaility or getting heads and the other one is biased with probability of getting heads. A coin is 2013Baye's Theorem
  40. 40An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each with one option being the correct2013Classical Definition of Probability
  41. 41Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets a2012Classical Definition of Probability
  42. 42An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is2012Classical Definition of Probability
  43. 43Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with pro2012Baye's Theorem
  44. 44Let and be two events with and Then is equal to2012Classical Definition of Probability
  45. 454 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is2011Classical Definition of Probability
  46. 46A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is2011Independent Events
  47. 47Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is2010Addition and Subtraction Theorems
  48. 48The probability that at least one of and occurs is 0.6 . If A and occur simultaneously with probability 0.3 , then is2010Addition and Subtraction Theorems
  49. 49and are two independent events such that and . The is2009Independent Events
  50. 50Three numbers are chosen at random from 1 to 20 . The probability that they are consecutive is2009Classical Definition of Probability

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 50 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Probability has appeared in 18 of the 18 years of WBJEE papers covered here, with 50 questions across 18 papers - about 3 per paper it appears in.

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

Of the 50 questions analysed for this chapter, 36% are easy, 58% moderate and 6% tough. 2015 had the most, with 6 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 20 questions (40%)
  • Addition and Subtraction Theorems - 7 questions (14%)
  • Conditional Probability and Multiplication Theorem - 7 questions (14%)
  • Classical Definition of Probability has produced the most tough questions (3).
6.Is Probability's weightage in WBJEE going up or down?

Across all 18 papers analysed, Probability has averaged about 2.8 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.