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Saturday, 10 October

JEE Main Maths · Class 12

Probability: JEE Main previous year questions

Probability had 49 questions in the 42 JEE Main shifts Lumi analysed, about 1.2 a shift, asked in 40 of 42 shifts. It ranks 11 of 22 Maths chapters by questions; 16% of its questions were hard.

Questions
49
in 40 of 42 shifts
A shift, on average
1.2
of 25 Maths questions
Since 2024
-0.3
1.3 a shift in 2017–23, 1.1 in 2024–26
Numerical answer
9
18% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06123’175’203’216’224’2311’248’259’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20173
  • 20205
  • 20213
  • 20226
  • 20234
  • 202411
  • 20258
  • 20269
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

7 topics and 17 distinct ideas; 3 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

26 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
3 repeat

Study it on Lumi

Probability: the interactive lesson

Every question

All 49 Probability questions

Newest first. Each opens with its options and the official answer.

2026 9 questions

  1. 2 Apr 2026, Shift 1 · Q23Let a,b,c∈{1,2,3,4}a, b, c \in \{1, 2, 3, 4\}. If the probability, that ax2+22 bx+c>0ax^2+2\sqrt2\,bx+c>0 for all x∈Rx \in \mathbf{R}, is mn\frac{m}{n},…MediumNumerical value
  2. 2 Apr 2026, Shift 2 · Q8A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q21A coin is tossed 88 times. If the probability that exactly 44 heads appear in the first six tosses and exactly 33 heads appear in the…HardNumerical value
  4. 4 Apr 2026, Shift 2 · Q21From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal…MediumNumerical value
  5. 5 Apr 2026, Shift 1 · Q7A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are…MediumSingle correct
  6. 5 Apr 2026, Shift 2 · Q8The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is…EasySingle correct
  7. 6 Apr 2026, Shift 1 · Q10A bag contains (N+1)(\mathrm{N}+1) coins −- N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed.…EasySingle correct
  8. 6 Apr 2026, Shift 2 · Q9A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each…MediumSingle correct
  9. 8 Apr 2026, Shift 2 · Q6A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the…EasySingle correct

2025 8 questions

  1. 2 Apr 2025, Shift 1 · Q25Three distinct numbers are selected randomly from the set {1,2,3,…,40}\{1, 2, 3, \ldots, 40\}. If the probability, that the selected numbers are in…HardNumerical value
  2. 2 Apr 2025, Shift 2 · Q9Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5 Bag II: Red 4, Blue 3,…EasySingle correctHas a figure
  3. 3 Apr 2025, Shift 1 · Q22All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the…HardNumerical value
  4. 3 Apr 2025, Shift 2 · Q8If the probability that the random variable XX takes the value xx is given by P(X=x)=k(x+1)3−x, x=0,1,2,3…P(X = x) = k(x + 1)3^{-x},\ x = 0, 1, 2, 3\ldots, where…MediumSingle correct
  5. 4 Apr 2025, Shift 2 · Q23A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of…MediumNumerical value
  6. 7 Apr 2025, Shift 2 · Q9Let a random variable XX take values 0,1,2,30, 1, 2, 3 with P(X=0)=P(X=1)=pP(X=0)=P(X=1)=p, P(X=2)=P(X=3)P(X=2)=P(X=3) and E(X2)=2E(X)E(X^2)=2E(X). Then the value of 8p−18p-1 is :MediumSingle correct
  7. 7 Apr 2025, Shift 2 · Q10A 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…MediumSingle correct
  8. 8 Apr 2025, Shift 2 · Q9If AA and BB are two events such that P(A)=0.7P(A) = 0.7, P(B)=0.4P(B) = 0.4 and P(A∩B‾)=0.5P(A \cap \overline{B}) = 0.5, where B‾\overline{B} denotes the…MediumSingle correct

2024 11 questions

  1. 6 Apr 2024, Shift 2 · Q20If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly…EasySingle correct
  2. 6 Apr 2024, Shift 2 · Q29From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable XX denote the number of…HardNumerical value
  3. 8 Apr 2024, Shift 1 · Q19Let the sum of two positive integers be 24. If the probability, that their product is not less than 34\frac{3}{4} times their greatest…MediumSingle correct
  4. 8 Apr 2024, Shift 1 · Q30Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables XX and YY respectively denote…MediumNumerical value
  5. 9 Apr 2024, Shift 1 · Q30Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,41,2,3,4. If the…MediumNumerical value
  6. 9 Apr 2024, Shift 2 · Q20If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ithi^{\text{th}} roll than the number…MediumSingle correct
  7. 29 Jan 2024, Shift 1 · Q19A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, isMediumSingle correct
  8. 30 Jan 2024, Shift 2 · Q20Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it.…EasySingle correct
  9. 31 Jan 2024, Shift 1 · Q17Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable xx to be the number of rotten apples in…MediumSingle correct
  10. 31 Jan 2024, Shift 1 · Q19Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made…EasySingle correct
  11. 31 Jan 2024, Shift 2 · Q19A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two…EasySingle correct

2023 4 questions

  1. 6 Apr 2023, Shift 1 · Q18A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is…MediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q17If the probability that the random variable XX takes values xx is given by P(X=x)=k(x+1)3−xP(X = x) = k(x + 1)3^{-x}, x=0,1,2,3,…x = 0, 1, 2, 3, \ldots, where…MediumSingle correct
  3. 11 Apr 2023, Shift 1 · Q17Let S={M=[aij], aij∈{0,1,2}, 1≤i,j≤2}S = \{M = [a_{ij}],\ a_{ij} \in \{0, 1, 2\},\ 1 \le i, j \le 2\} be a sample space and A={M∈S:M is invertible}A = \{M \in S : M \text{ is invertible}\}…HardSingle correct
  4. 13 Apr 2023, Shift 2 · Q19The random variable X follows binomial distribution B(n,p)(n, p), for which the difference of the mean and the variance is 11. If…MediumSingle correct

2022 6 questions

  1. 25 Jul 2022, Shift 1 · Q16If the sum and the product of mean and variance of a binomial distribution are 2424 and 128128 respectively, then the probability of one or…MediumSingle correct
  2. 25 Jul 2022, Shift 1 · Q17If the numbers appeared on the two throws of a fair six faced die are α\alpha and β\beta, then the probability that…MediumSingle correct
  3. 28 Jul 2022, Shift 1 · Q9Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is…EasySingle correct
  4. 24 Jun 2022, Shift 1 · Q4Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2…MediumSingle correct
  5. 24 Jun 2022, Shift 1 · Q17If a random variable X follows the Binomial distribution B(33, p) such that 3P(X=0)=P(X=1)3P(X=0)=P(X=1), then the value of…MediumSingle correct
  6. 29 Jun 2022, Shift 1 · Q1The probability that a randomly chosen 2×22\times 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :HardSingle correct

2021 3 questions

  1. 3 Aug 2021, Shift 2 · Q78A dice is thrown twice. If AA is the event that the sum of numbers appearing on them is 7 and BB is the event that number 5 appears at…EasySingle correct
  2. 25 Jul 2021, Shift 1 · Q74Let 9 distinct balls be distributed among 4 boxes, B1B_1, B2B_2, B3B_3 and B4B_4. If the probability that B3B_3 contains exactly 3 balls…MediumSingle correct
  3. 16 Mar 2021, Shift 2 · Q67Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of…MediumSingle correct

2020 5 questions

  1. 8 Jan 2020, Shift 1 · Q68Let A and B be two independent events such that P(A)=13P(A)=\frac{1}{3} and P(B)=16P(B)=\frac{1}{6}. Then, which of the following is TRUE ?MediumSingle correct
  2. 9 Jan 2020, Shift 2 · Q67A random variable X has the following probability distribution : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | K2K^2 | 2K2K…EasySingle correct
  3. 9 Jan 2020, Shift 2 · Q68If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3…MediumSingle correct
  4. 2 Sep 2020, Shift 1 · Q68Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn…MediumSingle correct
  5. 6 Sep 2020, Shift 2 · Q68The probabilities of three events A, B and C are given by P(A)=0.6P(A)=0.6, P(B)=0.4P(B)=0.4 and P(C)=0.5P(C)=0.5. If P(A∪B)=0.8P(A\cup B)=0.8, P(A∩C)=0.3P(A\cap C)=0.3,…HardSingle correct

2017 3 questions

  1. 2 Apr 2017 (offline) · Q85A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number…EasySingle correct
  2. 2 Apr 2017 (offline) · Q86For three events A, B and C, P(Exactly one of A or B occurs) == P(Exactly one of B or C occurs) == P(Exactly one of C or A occurs)…HardSingle correct
  3. 2 Apr 2017 (offline) · Q87If two different numbers are taken from the set {0,1,2,3,……,10}\{0,1,2,3,\ldots\ldots,10\}; then the probability that their sum as well as absolute…MediumSingle correct

Pattern: Asked most years.