JEE Advanced Probability (Class 12) — previous year questions
38 questions from 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007.
- Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green…
- A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6…
- Three students S₁, S₂, and S₃ are given a problem to solve. Consider the following events: U: At least one of…
- A factory has a total of three manufacturing units M₁, M₂ and M₃, which produce bulbs independent of each…
- A student appears for a quiz consisting of only true-false type questions and answers all the questions. The…
- A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue.…
- Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that…
- Let X = {(x,y) ∈ Z × Z : x²/8 + y²/20 < 1 and y² < 5x}. Three distinct points P, Q and R are randomly chosen…
- Let X be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in X while 02244…
- Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If…
- Let pᵢ be the probability that a randomly chosen point has i many friends, i=0,1,2,3,4. Let X be a random…
- Two distinct points are chosen randomly out of the points A₁, A₂, …, A₄₉. Let p be the probability that they…
- Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are…
- Consider three sets E₁ = {1, 2, 3}, F₁ = {1, 3, 4} and G₁ = {2, 3, 4, 5}. Two elements are chosen at random,…
- Let C₁ and C₂ be two biased coins such that the probabilities of getting head in a single toss are 2/3 and…
- The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely,…
- Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers…
- Let S be the sample space of all 3 × 3 matrices with entries from the set {0,1}. Let the events E₁ and E₂ be…
- Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each…
- There are three bags B₁, B₂, and B₃. The bag B₁ contains 5 red and 5 green balls, B₂ contains 3 red and 5…
- Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z = 10. Then…
- Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2 and P(Y|X)=2/5. Then
- A computer producing factory has only two plants T₁ and T₂. Plant T₁ produces 20% and plant T₂ produces 80%…
- The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two…
- Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at…
- Of the three independent events E1, E2 and E3, the probability that only E1 occurs is α, only E2 occurs is β…
- Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then the…
- Four fair dice D₁, D₂, D₃ and D₄; each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled…
- Let X and Y be two events such that P(X|Y)=1/2, P(Y|X)=1/3 and P(X∩ Y)=1/6. Which of the following is(are)…
- A ship is fitted with three engines E₁, E₂ and E₃. The engines function independently of each other with…
- Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the…
- A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and…
- Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the…
- An experiment has 10 equally likely outcomes. Let A and B be non-empty events of the experiment. If A…
- Consider the system of equations ax + by = 0; cx + dy = 0, where a, b, c, d ∈ {0, 1} STATEMENT I : The…
- Let Eᶜ denote the complement of an event E. Let E, F, G be pairwise independent events with P(G) > 0 and P(E…
- One Indian and four American men and their wives are to be seated randomly around a circular table. Then the…
- Let H₁, H₂, …, Hₙ be mutually exclusive and exhaustive events with P(Hᵢ) > 0, i = 1, 2, …, n. Let E be any…