Jump to a section

Mathematics - Probability

Practise 108 NTA Abhyas (JEE Main) questions on Probability. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Probability has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 108 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Probability that A will pass the exam is 1 4 , B will pass the exam is 2 5 and C will pass the exam is 2 3 . The probability that exactly on
  2. 22 dice are thrown. Suppose a random variable X is assigned a value 2 k , if the sum on the dice is equal to k , then the expected value of X
  3. 3A multiple-choice question has 5 options of which only one is correct. If a student does home work, then he is sure to identify the correct
  4. 4If two distinct numbers a and b are selected from the set 5 1 , 5 2 , 5 3 . . . . . . . 5 9 , then the probability that log a b is an intege
  5. 5A bag contains a mixed lot of red and blue balls. If two balls are drawn at random, the probability of drawing two red balls is five times t
  6. 6Two persons A and B have equal number of sons. There are three cinema tickets which are to be distributed among sons of A and B . The probab
  7. 7A bag contains 21 markers with numbers 1 to 21 . A marker is drawn at random and then replaced and then a second marker is drawn. The probab
  8. 8Fifteen coupons are numbered 1, 2, 3 , … . . , 15 respectively. Seven coupons are selected at random one at a time with replacement. The pro
  9. 9If 4 distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all 4 of them are either divisible b
  10. 10The probability of a bomb hitting a bridge is 2 3 . Two direct hits are needed to destroy the bridge. The minimum number of bombs required s
  11. 11Three balls are marked with 2 , 4 and 6 . They are placed in a box and a ball is drawn, its number is noted and the ball drawn is returned t
  12. 12The probability of a problem being solved by 3 students independently are 1 2 , 1 3 and α respectively. If the probability that the problem
  13. 134 different balls of green colour and 4 different balls of red colour are to be distributed equally among 4 people. The probability that all
  14. 14If letters of the word R E G U L A T I O N S are randomly arranged, then the probability that there are exactly four letters between R and S
  15. 15Out of 1000 boys in a school, 300 played cricket, 380 played hockey and 420 played basketball. Of the total, 120 played both basketball and
  16. 16Each of A and B tosses a fair coin simultaneously 10 times. The probability that both of them will not get tail at the same toss is equal to
  17. 17Consider an experiment of a single throw of a pair of unbiased normal dice. Let three events ε 1 , ε 2 and ε 3 are defined as follows ε 1 :
  18. 18A biased coin is tossed repeatedly until a tail appears for the first time. The head is 3 times likely to appear as the tail. The probabilit
  19. 19A fair coin is tossed once. If it shows head, then 2 fair dice are thrown simultaneously otherwise 3 fair dice are thrown simultaneously. Th
  20. 20If A , B , C are three events such that P B = 4 5 , P A B C c = 1 4 and P A c B C c = 1 3 , then P B C is equal to
  21. 21Two dice are thrown at a time, the probability that the absolute value of the difference of number on dice is 3 , is
  22. 22If x = 33 n , n is a positive integral value, then the probability that x will have 3 at its units place is
  23. 23In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he
  24. 24The 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, is
  25. 25The probability distribution of a random variable X is P X = X 12 : X = 1,2 , 3,4 , 5,6 0 : otherwise . Then, the conditional probability P
  26. 26Two natural numbers are randomly chosen and multiplied, then the chance that their product is divisible by 3 is
  27. 27Six fair dice are rolled. The probability that the product of the numbers appearing on top faces is prime, is
  28. 28An experiment yields 3 mutually exclusive and exhaustive events A , B and C . If P A = 2 P ( B ) = 3 P C , then P A is equal to
  29. 29Dice A has 4 red and 2 white faces whereas dice B has 3 red and 3 white faces. A coin is tossed once, if it falls head then the game continu
  30. 30A 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 pr
  31. 31An unbiased die is rolled n times. Let P A , P B and P C be the probability of occurrence of an odd number exactly one, two and three times
  32. 32A small pack of cards consists of 5 green cards, 4 blue cards and 3 black cards. The pack is shuffled through and first three cards are turn
  33. 33Shubham has 75 % chance of attending the annual meet. Shikha has a 90 % chance if Shubham also attends otherwise she has a 40 % chance of at
  34. 34Two numbers are selected randomly from set S = 1,2 , 3,4 , 5,6 without replacement one by one. The probability that a minimum of two number
  35. 35A box contains x red balls and 10 black balls. 3 balls are drawn one by one without replacement. If the probability of choosing 3 red balls
  36. 36A card is lost from a pack of 52 playing cards. From the remainder of the pack, one card is drawn and is found to be spade. The probability
  37. 37A fair coin is tossed repeatedly until two consecutive heads are obtained. If the probability that 2 consecutive heads occur on fourth and f
  38. 38A person goes to the office either by a car, or scooter, or bus, the probability of which being 2 7 , 3 7 , 2 7 respectively. The probabilit
  39. 39A purse contains 10 ten rupee coins and 5 five rupee coins. Two coins are randomly drawn. If the expected value of 2 drawn coins is λ , then
  40. 40A term is randomly chosen from the expansion of 4 6 + 1 5 4 20 . If the probability that it is a rational term is P , then 420 P is equal to
  41. 41The probability distribution of a random variable X is given as X − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 P ( X ) p 2 p 3 p 4 p 5 p 7 p 8 p 9 p 10 p
  42. 42Mr. Vipin, a famous liar, is known to speak the truth 5 out of 6 times. His blind folded friend Shubham throws a pair of dice and asked Vipi
  43. 43A biased coin that has a probability of getting heads as p ( 0 p 1 ) is tossed until a head appears for the first time. If the probability t
  44. 44A random variable X follows binomial probability distribution with probability P ( X ) , with mean as 2 , probability of success as p and pr
  45. 45Three boxes are labeled as A , B and C and each box contains 5 balls numbered 1 , 2 , 3, 4 and 5 . The balls in each box are well mixed and
  46. 46A committee of 5 persons is to be randomly selected from a group of 5 men and 4 women and a chairperson will be randomly selected from the c
  47. 47A man alternately tosses a coin and throw a dice, beginning with the coin. The probability that he gets a head in coin before he gets a 5 or
  48. 48An unbiased die is rolled until a number greater than 4 appears. The probability that an even number of trials are needed, is
  49. 49Given two independent events, if the probability that both the events occur is 8 49 , the probability that exactly one of them occurs is 26
  50. 5015 coins are tossed. If the probability of getting at least 8 heads is equal to p , then 8 p is equal to

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 108 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Probability questions in NTA Abhyas (JEE Main)?

Of the 108 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Probability should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.