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Mathematics - Probability

Practise 392 MHTCET previous year questions on Probability, compiled from papers spanning 2007 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 MHTCET tests.

Probability has been asked in 17 of the 17 years of MHTCET papers analysed (2007–2026), with 392 questions in all. 37% of them were easy, 54% moderate and 9% tough. Most of its questions came from 2025, with 64 questions that year. In the last three years (2024–2026) it had 175 questions across 59 papers, about 3 per paper.

The chapter's 9 topics are not weighted equally: Random Variable and its Probability Distribution (169 questions, 43%), Bernoulli Trial and Binomial Distribution (78 questions, 20%), and Classical Definition of Probability (71 questions, 18%) have been asked the most. Random Variable and its Probability Distribution has also led over the last five years, with 106 questions. Random Variable and its Probability Distribution has produced the most tough questions (19).

  1. 1In a certain city, the ratio of men to women is . It is found that of men and of women are literate. If a person selected at random is found20 Apr, 2026 (M)Baye's Theorem
  2. 2Let X be a continuous random variable with the probability density function(p.d.f.) given by P(2 < X 3) = $20 Apr, 2026 (M)Random Variable and its Probability Distribution
  3. 3A random variable follows a binomial distribution with . If , then the probability of success is..20 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  4. 4A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 20 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  5. 5For the following probability distribution of a random variable , the Expected value and Variance of are respectively20 Apr, 2026 (E)Random Variable and its Probability Distribution
  6. 6Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club ca20 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  7. 7Consider a game of tossing a six sided fair die. If the face that comes up is , the player wins Rs. and he loses Rs. , where is the face tha19 Apr, 2026 (M)Random Variable and its Probability Distribution
  8. 8Given the probability density function (p.d.f.) of the random variable X, , , otherwise, then which of the following is correct ?19 Apr, 2026 (M)Random Variable and its Probability Distribution
  9. 9If in trials, X is a binomial random variable which follows the relation , then the probability of failure is...19 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  10. 10Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in 19 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  11. 11Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 & 3. If X denotes the sum of the numbers, then the expec19 Apr, 2026 (E)Random Variable and its Probability Distribution
  12. 12The probability that a bomb will hit the target is . Out of 6 bombs dropped, probability that at least 1 will miss the target is...19 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  13. 13If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are , and respectively, while the probability o18 Apr, 2026 (M)Addition and Subtraction Theorems
  14. 14Let be the cumulative distribution function (c.d.f.) of a continuous random variable . If and , then the value of is ...18 Apr, 2026 (M)Random Variable and its Probability Distribution
  15. 15A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful pr18 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  16. 16In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. Th18 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  17. 17If the p. d. f. of a continuous random variable X is given by then the value of is18 Apr, 2026 (E)Random Variable and its Probability Distribution
  18. 18A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at18 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  19. 19A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green 17 Apr, 2026 (M)Random Variable and its Probability Distribution
  20. 20If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?17 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  21. 21Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______17 Apr, 2026 (E)Classical Definition of Probability
  22. 22If a discrete random variable takes the values such that , then17 Apr, 2026 (E)Random Variable and its Probability Distribution
  23. 23On average, one out of 10 persons is busy. If six persons are selected at random, then the probability that at least 5 of them will be busy 17 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  24. 24Two dice are thrown successively 4 times and getting a doublet is called a success. The probability of getting at least 1 success is16 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  25. 25The probability distribution of a random variable X is given by Then the c.d.f. of X is given by16 Apr, 2026 (M)Random Variable and its Probability Distribution
  26. 26A random variable X has the probability distribution for the events E = {X is a prime number} and F = {X 3}, then P (E F)=16 Apr, 2026 (M)Random Variable and its Probability Distribution
  27. 27Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the pro16 Apr, 2026 (M)Independent Events
  28. 28A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that th16 Apr, 2026 (M)Classical Definition of Probability
  29. 29If and are equally likely, mutually exclusive and exhaustive events and , , then equal to...16 Apr, 2026 (E)Baye's Theorem
  30. 30If a random variable has a probability mass function , then the mean of is ...16 Apr, 2026 (E)Random Variable and its Probability Distribution
  31. 31If a fair coin is tossed 8 times, then the probability of getting at most 2 heads is...16 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  32. 32If A and B are two events such that , and , then15 Apr, 2026 (M)Conditional Probability and Multiplication Theorem
  33. 33The Variance of the following probability distribution of X is X P(X) where15 Apr, 2026 (M)Random Variable and its Probability Distribution
  34. 34The centers for disease control have determined that when a person is given a vaccine, the probability that the person will develop immunity15 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  35. 35The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least o15 Apr, 2026 (E)Independent Events
  36. 36A random variable X has the following probability distribution X 1 2 3 4 5 6 7 8 P(X= ) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For the even15 Apr, 2026 (E)Random Variable and its Probability Distribution
  37. 37For the following probability distribution, the standard deviation of the random variable X is X 2 3 4 p(X= ) 0.2 0.5 0.315 Apr, 2026 (E)Random Variable and its Probability Distribution
  38. 38Let . Then the maximum probability occurs at13 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  39. 39A random variable X takes the values 0, 1, 2, 3 and its mean is . If and , then is13 Apr, 2026 (M)Random Variable and its Probability Distribution
  40. 40A random variable X has the following probability distribution For the events , , is13 Apr, 2026 (M)Random Variable and its Probability Distribution
  41. 41The odds in favour of A winning a game of table tennis against B are 1:2. If 3 games are to be played, then the probability of A winning at 13 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  42. 42A certain disease has a prevalence of in the population. A diagnostic test for the disease has a sensitivity of and a specificity of . If a 13 Apr, 2026 (E)Baye's Theorem
  43. 43It is known that a box of batteries contains defective pieces and a person randomly selects batteries from this box. Then the probability di13 Apr, 2026 (E)Classical Definition of Probability
  44. 44In a multiple-choice examination, there are questions with one correct option out of options for each question. A student gets marks for eac13 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  45. 45Two cards are drawn at random from a standard pack of cards. Then the probability that the draw consists of exactly one face card and exactl11 Apr, 2026 (M)Classical Definition of Probability
  46. 46If the following function is probability density function of r.v. X , for , otherwise, then the value of is11 Apr, 2026 (M)Random Variable and its Probability Distribution
  47. 47Let . If and , then the probability of getting at most one success is .....11 Apr, 2026 (M)Bernoulli Trial and Binomial Distribution
  48. 48If events A and B are such that , and then ...........11 Apr, 2026 (E)Conditional Probability and Multiplication Theorem
  49. 49The probability mass function of a random variable X is given by , for and , otherwise. Then which of the following is correct?11 Apr, 2026 (E)Bernoulli Trial and Binomial Distribution
  50. 50A player tosses two fair coins, he wins Rs. if two heads appear, Rs. if one head appears and Rs. if no head appears, then the variance of th11 Apr, 2026 (E)Random Variable and its Probability Distribution

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 392 questions compiled from MHTCET papers spanning 2007 to 2026.

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

These are MHTCET 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 MHTCET Mathematics?

Probability has appeared in 17 of the 17 years of MHTCET papers covered here, with 392 questions across 107 papers - about 4 per paper it appears in.

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

Of the 392 questions analysed for this chapter, 37% are easy, 54% moderate and 9% tough. 2025 had the most, with 64 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Random Variable and its Probability Distribution - 169 questions (43%)
  • Bernoulli Trial and Binomial Distribution - 78 questions (20%)
  • Classical Definition of Probability - 71 questions (18%)
  • Random Variable and its Probability Distribution has produced the most tough questions (19).
6.Is Probability's weightage in MHTCET going up or down?

Across all 107 papers analysed, Probability has averaged about 3.7 questions per paper. In the last three years (2024–2026), that average has fallen, 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.