JEE Mathematics

Probability Distributions: JEE Questions & Solutions

21 previous-year JEE Mathematics questions on Probability Distributions, each with a worked step-by-step solution.

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Previous-year questions

  1. 01A random variable X takes values 0, 1, 2, 3 with probabilities (2a+1)/30, (8a-1)/30, (4a+1)/30, b respectively, where a, b ∈ ℝ. Let μ and σ…MCQMediumJEE 2026
  2. 02If a random variable x has the probability distribution | x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---|---| | P(x)…MCQMediumJEE 2026
  3. 03From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of…MCQEasyJEE 2026
  4. 04The probability distribution of a random variable X is given below: x 4k 30k/7 32k/7 34k/7 36k/7 38k/7 40k/7 6k P(X) 2/15 1/15 2/15 1/5…MCQMediumJEE 2026
  5. 05A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ² denote the mean and variance of X, then…MCQMediumJEE 2025
  6. 06Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between…MCQMediumJEE 2025
  7. 07Let A = [a_ij] be a 2 × 2 matrix such that a_ij ∈ {0, 1} for all i and j. Let the random variable X denote the possible values of the…MCQMediumJEE 2025
  8. 08All 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…NVAMediumJEE 2025
  9. 09If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3^(-x), x = 0, 1, 2, 3, …, where k is a…MCQMediumJEE 2025
  10. 10A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then…MCQMediumJEE 2025
  11. 11Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3), and E(X²) = 2E(X). Then the value of 8p -…MCQMediumJEE 2025
  12. 12Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a…MCQMediumJEE 2024
  13. 13Three rotten apples are accidentally mixed with seven good apples, and four apples are drawn one by one without replacement. Let the random…MCQMediumJEE 2023
  14. 14In a binomial distribution B(n, p), the sum and product of the mean and variance are 5 and 6, respectively. Then 6(n + p - q) is equal to:MCQMediumJEE 2023
  15. 15A 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…MCQMediumJEE 2023
  16. 16Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine…MCQMediumJEE 2023
  17. 17Let the probability of getting a head for a biased coin be 1/4. It is tossed repeatedly until a head appears. Let N be the number of tosses…NVAMediumJEE 2023
  18. 18Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is p/q, where p and q…MCQMediumJEE 2023
  19. 19A fair n > 1 faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is n/9, then n…NVAMediumJEE 2023
  20. 20A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or 3 tails occur. If X denotes…MCQMediumJEE 2023
  21. 21The random variable X follows binomial distribution B(n, p), for which the difference of the mean and the variance is 1. If 2P(X = 2) =…MCQMediumJEE 2023

Frequently asked questions

Our bank has 21 previous-year JEE Mathematics questions tagged to Probability Distributions, drawn from JEE papers between 2023 and 2026, including 4 from 2026 alone. Each comes with a full step-by-step solution.

Probability Distributions is rated Advanced overall for JEE Mathematics. The PYQs on this page break down as 20 medium, 1 easy.

Of the 21 previous-year questions on Probability Distributions, 18 are multiple-choice (MCQ) and 3 are numerical-value (NVA) questions.

Based on recent paper analysis, Probability Distributions is worth about 1 mark in JEE Main. It sits in Statistics & Probability, a Class 11 Mathematics chapter.

More Statistics & Probability topics

Probability Basics32Measures of Dispersion30Conditional Probability & Bayes Theorem15Measures of Central Tendency10

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