JEE Advanced Probability questions with solutions
Conditional probability, Bayes theorem and distributions. 42 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
Also practise: Probability for JEE Main · Probability for CAT · Probability for NDA
JEE Advanced 2025
- A fair die is rolled once and shows the number n. Then n fair coins are tossed. Given that exactly two heads appear, the probability that n was a…
- A number a is chosen at random (uniformly) from the interval [0,3] and independently a number b is chosen at random (uniformly) from [0,2]. Find the…
- Players A and B throw a fair die alternately, A first. A wins at once if his throw shows 6; B wins at once if his throw shows 4, 5 or 6. Given that…
- If the outcome is 1 or 2, two balls are drawn without replacement from urn A containing 3 red and 2 blue balls; otherwise two balls are drawn without…
- The probability that the experiment stops at an even-numbered toss is ______.
JEE Advanced 2024
- An urn UA has 3 red and 2 blue balls, and an urn UB has 2 red and 4 blue balls. A fair die is rolled; if the number is 1 or 2, urn UA is chosen…
- Three fair six-faced dice are rolled together. The probability that the product of the three numbers shown is divisible by 12 is m/n, where m and n…
- A fair die is thrown once. If the result is 1 or 2, two balls are drawn without replacement from Urn I containing 3 red and 2 blue balls; otherwise…
- Paragraph 2: Let X denote the number of tosses required. It is known that the number of head-tail sequences of length n≥2 that end in HH (for n≥3, in…
JEE Advanced 2023
JEE Advanced 2022
- Urn A contains 3 red and 2 blue balls; urn B contains 2 red and 4 blue balls. if the number is 1 or 2 urn A is chosen, otherwise urn B. Two balls are…
- Players A and B throw a fair die alternately, A going first, and the first player to throw a six wins. Given that the game is decided within the…
- Two fair dice are thrown. Let X be the event that the product of the numbers is even, Y the event that the sum is a multiple of 3, Z the event that…
JEE Advanced 2021
- A fair die is rolled once. If the number shown is 1 or 2, two balls are drawn together (without replacement) from bag A containing 3 red and 2 blue…
- Paragraph 2: Two players A and B take turns rolling one fair die, with A rolling first, then B, then A, and so on. Player A wins immediately if A…
- Three fair dice are rolled. Given that the sum of the three numbers is a multiple of 4, the probability that their product is divisible by 4 is p/q…
- A fair die is rolled. If the result is 1 or 2, two balls are drawn without replacement from bag A containing 3 red and 2 blue balls; otherwise two…
- Paragraph 2: Let X be the total number of tosses made. Each toss is independent of the others, and the process stops as soon as the pattern HH…
JEE Advanced 2020
- Box I contains 3 red and 2 blue balls; Box II contains 4 red and 1 blue ball. One ball is chosen at random from Box I and placed in Box II. Then two…
- A fair die is rolled once. If it shows 1 or 2, two balls are drawn without replacement from urn U1 containing 2 white and 3 black balls; otherwise…
- A fair die is rolled three times. Let X and Y denote the largest and the smallest of the three numbers obtained.
- A coin with P(head)=3/5 is tossed repeatedly until the pattern head, tail, head (HTH) appears for the first time as three consecutive tosses. Find…
JEE Advanced 2019
- Box I contains 4 white and 2 black balls; Box II contains 2 white and 4 black balls. if the outcome is 1 or 2, two balls are drawn one after the…
- A particle starts at the point 3 on the set \0,1,2,…,8\. At each step it moves one unit to the right with probability 0.6 and one unit to the left…
- Box B1 contains 4 red and 2 white balls; box B2 contains 2 red and 4 white balls. A fair coin is tossed: on heads B1 is chosen, on tails B2. Two…
- A fair die is rolled repeatedly until the first six appears. Let X be the number of rolls required. Then the conditional expectation E[Xmid X is…
JEE Advanced 2018
- Urn UA contains 3 red and 2 blue balls and urn UB contains 2 red and 3 blue balls. A fair die is rolled; if the number is 1 or 2 the urn UA is…
- A coin shows heads with probability 2/3 on each independent toss. It is tossed repeatedly until the pattern H, T, H (heads, tails, heads in…
- A number is chosen at random from \1,2,…,60\. Let A, B, C be the events that the number is divisible by 2, by 3 and by 4 respectively.
- Match the experiments in List-I with their probabilities in List-II. List-I (P) A fair die is thrown three times. The probability that the three…
JEE Advanced 2017
- A fair coin is tossed 6 times. Let E be the event that no two consecutive tosses are both heads, and F the event that exactly three heads occur.
- Urn A contains 3 red and 2 black balls; urn B contains 2 red and 4 black balls. if the number is 1 or 2 urn A is chosen, otherwise urn B is chosen.…
- Three fair six-faced dice are rolled together.
JEE Advanced 2016
- A fair die is thrown once. If the number is 1 or 2, two balls are drawn one after another without replacement from bag A containing 3 red and 2 blue…
- A fair coin is tossed repeatedly until the three consecutive outcomes head, tail, tail (in this order) appear for the first time. The expected number…
- A fair die is rolled. If the number obtained is 1 or 2, two balls are drawn one after another without replacement from urn U1 containing 5 red and 3…
- Two players A and B throw a fair die alternately, A throwing first; the first player to throw a six wins the game.
Other Mathematics topics
Area Under Curves 13Binomial Theorem 10Complex Numbers 24Conic Sections 34Differential Equations 18Differentiation and Application of Derivatives 20Indefinite and Definite Integrals 18Limits 19Matrices and Determinants 28Permutations and Combinations 18Quadratic Equations 12Sequences and Series 11Sets, Relations and Functions 8Straight Lines and Circles 10Three Dimensional Geometry 22Trigonometry and Inverse Trigonometric Functions 18Vector Algebra 9