JEE Mathematics
Probability Basics: JEE Questions & Solutions
32 previous-year JEE Mathematics questions on Probability Basics, each with a worked step-by-step solution.
Basic
Previous-year questions
- 01Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, where x > y, be 8 and 16 respectively. Two numbers are chosen from {1,…MCQMediumJEE 2026
- 02Two distinct numbers a and b are selected at random from 1, 2, 3, …, 50. The probability that their product ab is divisible by 3 isMCQEasyJEE 2026
- 03From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a - b…NVAMediumJEE 2026
- 04Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from bag B and…MCQEasyJEE 2026
- 05Let S be a set of 5 elements and P(S) denote the power set of S. Let E be the event of choosing an ordered pair (A,B) from P(S)× P(S) such…NVAEasyJEE 2026
- 06One die has two faces marked 1, two faces marked 2, one face marked 3, and one face marked 4. Another die has one face marked 1, two faces…MCQMediumJEE 2025
- 07A board has 16 squares as shown in the figure. Out of these 16 squares, two squares are chosen at random. The probability that they have no…MCQEasyJEE 2025
- 08A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8…MCQMediumJEE 2025
- 09Let A = [a_ij] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then the…MCQEasyJEE 2025
- 10Two numbers k₁ and k₂ are randomly chosen from the set of natural numbers. Then, the probability that the value of i^k₁ + i^k₂ (where i =…MCQEasyJEE 2025
- 11Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected…MCQEasyJEE 2025
- 12Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1…MCQMediumJEE 2025
- 13Three distinct numbers are selected randomly from the set {1, 2, 3, …, 40}. If the probability that the selected numbers are in an…NVAMediumJEE 2025
- 14The probability of forming a 12 persons committee from 4 engineers, 2 doctors, and 10 professors containing at least 3 engineers and at…MCQMediumJEE 2025
- 15A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required, and let a = P(X = 3), b = P(X ≥ 3),…MCQMediumJEE 2024
- 16An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability that the first…MCQMediumJEE 2024
- 17A fair die is thrown until the number 2 appears. What is the probability that 2 appears in an even number of throws?MCQMediumJEE 2024
- 18An integer is chosen at random from the integers 1, 2, 3, …, 50. The probability that the chosen integer is a multiple of at least one of…MCQMediumJEE 2024
- 19Two integers x and y are chosen with replacement from the set {0,1,2,…,10}. Then the probability that |x - y| > 5 is:MCQEasyJEE 2024
- 20Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles, with replacement being made…MCQEasyJEE 2024
- 21The coefficients a, b, and c in the quadratic equation ax² + bx + c = 0 are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}. The probability…MCQMediumJEE 2024
- 22If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i-th roll than the number obtained in the…MCQMediumJEE 2024
- 23If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly…MCQMediumJEE 2024
- 24Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, √3N, N+2 are in geometric…MCQMediumJEE 2023
- 25Let S = {W₁, W₂, …} be the sample space associated with a random experiment. Let P(Wₙ) = P(Wₙ₋₁)/2, n ≥ 2. Let A = {2k + 3l; k, l ∈ ℕ} and…MCQMediumJEE 2023
- 26If an unbiased die, marked with -2, -1, 0, 1, 2, 3 on its faces, is thrown five times, then the probability that the product of the…MCQMediumJEE 2023
- 27A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are…NVAMediumJEE 2023
- 28Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space [0, 60] is less than or equal…NVAMediumJEE 2023
- 29Two dice are thrown independently. Let A be the event that the number appeared on the 1^st die is less than the number appeared on the 2^nd…MCQMediumJEE 2023
- 30Three dice are rolled. If the probability of getting different numbers on the three dice is p/q, where p and q are co-prime, then q - p is…MCQEasyJEE 2023
- 31Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2N < N! is m/n, where m and n are coprime,…MCQEasyJEE 2023
- 32A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn…MCQMediumJEE 2023
Frequently asked questions
Our bank has 32 previous-year JEE Mathematics questions tagged to Probability Basics, drawn from JEE papers between 2023 and 2026, including 5 from 2026 alone. Each comes with a full step-by-step solution.
Probability Basics is rated Basic overall for JEE Mathematics. The PYQs on this page break down as 21 medium, 11 easy.
Of the 32 previous-year questions on Probability Basics, 27 are multiple-choice (MCQ) and 5 are numerical-value (NVA) questions.
Based on recent paper analysis, Probability Basics is worth about 2 marks in JEE Main. It sits in Statistics & Probability, a Class 11 Mathematics chapter.
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