Probability is among the most important topics, having a weightage of around 14-15% in the JEE Advanced Exam 2025.
The topics covered under probability include random experiments, sample space, various types of events (impossible, simple, compound), addition and multiplication rule of probability, conditional probability, independence of events, total probability, Bayes Theorem, determination of probability of events through permutations and combinations.
Key concepts like Bayes Theorem and Conditional probability are repeatedly asked in JEE Advanced question papers, and therefore this chapter needs to be practiced to perform good in the exam.
Must Read Articles:
- Download JEE Advanced Last 10 year PYQ for Free
- Download JEE 2024 Question Paper with Detailed Solutions
Listed below the most repeated questions JEE Advanced Previous Year Questions (PYQs) on Probability along with detailed solutions -
Question 1:
A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For i = 1, 2, 3, let Wi, Gi and Bi denote the events that the ball drawn in the ith draw is a white ball, green ball, and blue ball, respectively. If the probability
P(W1∩G2∩B3)=25N and the conditional probability P(B3∣W1∩G2)=29, then N equals ________.
Question 2:
Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy -plane, and P(X = x) = 0 for all x ∈ R - {0,1,2,3,4}. If the mean of X is 5/2 , and the variance of X is α, then the value of 24α is ______.
Question 3:
A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 1/2. Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is 1/6. Then the probability that the student knows the answer of a randomly chosen question is-
Question 4:
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are the same. If the probability of a random toss resulting in a head is 1/3, then the probability that the experiment stops with the head is-
Question 5:
Let X be the set of all five-digit numbers formed using 1,2,2,2,2,4,4,0. for example 22240 is in X while 02244 and 44422 are not in X. Suppose that each element of X has an equal chance of being chosen. Let p be the conditional probability that a component chosen at random is a multiple of 20 given that it is a multiple of 5. Then the numerous of 38p is equal to
Question 6:
Consider the 6 x 6 square in the figure. Let A1, A2, ........, A49 be the points of intersections (dots in the picture) in some order. We say that Ai and Aj are friends if they are adjacent along a row or a column. Assume that each point Ai has an equal chance of being chosen. Two distinct points are chosen randomly out of the points A1, A2, ........, A49. Let p be the probability that they are friends. Then the value of 7p is
Question 7:
Two players, P1 and P2, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P1 and P2, respectively. If x > y, then P1 scores 5 points and P2 scores 0 point. If x = y, then each player scores 2 points. If x < y, then P1 scores 0 point and P2 scores 5 points. Let Xi and Yi be the total scores of P1 and P2, respectively, after playing the ith round.
| List-I | List-II | ||
|---|---|---|---|
| I | Probability of (X2 ≥ Y2) is | P | 3883 |
| II | Probability of (X2 > Y2) is | Q | 11161611 |
| III | Probability of (X3 = Y3) is | R | 516165 |
| IV | Probability of (X3 > Y3) is | S | 355864864355 |
| T | 7743243277 | ||
The correct option is:
Question 8:
In a study about a pandemic, data of 900 persons was collected. It was found that
190 persons had symptom of fever,
220 persons had symptom of cough,
220 persons had symptom of breathing problem,
330 persons had symptom of fever or cough or both,
350 persons had symptom of cough or breathing problem or both,
340 persons had symptom of fever or breathing problem or both,
30 persons had all three symptoms (fever, cough and breathing problem).
If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is _____________.
Question 9:
Suppose that
Box-I contains 8 red, 3 blue and 5 green balls,
Box-II contains 24 red, 9 blue and 15 green balls,
Box-III contains 1 blue, 12 green and 3 yellow balls,
Box-IV contains 10 green, 16 orange and 6 white balls.
A ball is chosen randomly from Box-I ; call this ball b If b is red then a ball is chosen randomly from Box-II, if b is blue then a ball is chosen randomly from Box-III, and if b is green then a ball is chosen randomly from Box-IV The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened, is equal to
Question 10:
A number is chosen at random from the set {1,2,3,…,2000} Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is_____
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination was conducted ONLY in the Computer Based Test (CBT) mode.
- Number of papers: Two question papers: Paper 1 and Paper 2 of three hours duration each. Both papers are compulsory.
- Language: English and Hindi
- Total duration: 6 hours
- Number of sections: Each question paper consisted of three separate sections, viz., Physics, Chemistry and Mathematics.
- Marking scheme: Details of the marking scheme were provided in the “Instructions to Candidates” section at the time of examination. The same is also explained further below.
JEE Advanced 2025 Mathematics Syllabus
JEE Advanced Mathematics Syllabus consists of nine units- Sets, Relations and Functions ; Algebra ; Matrices; Probability and Statistics; Trignometry; Analytical Geometry; Differential Calculus ; Integral Calculus and Vectors. Check JEE Advanced 2025 Syllabus
JEE Advanced Mathematics Syllabus according to the seven units is defined below.
| Units | Sub Units |
|---|---|
| Sets, Relations, and Functions | - Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for finite number of sets), and practical problems based on them.- Cartesian product of finite sets, ordered pair, relations, domain, and codomain of relations, equivalence relation.- Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions. |
| Algebra | - Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.- Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.- Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.- Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients. |
| Matrices | - Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | - Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.- Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. |
| Trigonometry | - Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.- Inverse trigonometric functions (principal value only) and their elementary properties. |
| Analytical Geometry | - Topics related to coordinate geometry, straight lines, circles, conic sections, and other geometric properties. |
| Differential Calculus | - Concepts of limits, continuity, differentiation, derivatives of functions, application of derivatives, increasing and decreasing functions, maxima and minima. |
| Integral Calculus | - Indefinite and definite integrals, properties of integrals, fundamental theorem of calculus, methods of integration, applications of integration. |
| Vectors | - Vectors and their properties, operations on vectors, scalar and vector products, applications in geometry and physics. |
JEE Advanced Mathematics Chapter-wise Weightage
However, based on the previous year's analysis, the chapters along with the number of questions and marks tabulated below:
| Chapter Name | Number of Questions | Marks |
|---|---|---|
| Application of Derivatives | 3 | 9 |
| Ellipse | 1 | 3 |
| Circles | 2 | 6 |
| Parabola | 2 | 7 |
| Definite Integral | 2 | 7 |
| Permutations and Combinations | 1 | 3 |
| Sequence and Series | 1 | 3 |
| Matrices | 2 | 7 |
| Limit and Continuity | 1 | 4 |
| Probability | 1 | 4 |
| Complex Numbers | 1 | 4 |
| Hyperbola | 1 | 4 |
JEE Advanced - Marks wise Weightage of Topics
| Topics | Marks |
|---|---|
| Calculus | 40-50 marks |
| Vector and 3D Geometry | 15-20 marks |
| Probability & Permutation & Combination | 15-20 marks |
| Parabola, Hyperbola, Ellipse, Rectangular Hyperbola | 15 marks |
| Complex Numbers | 15 marks |
Important Books for Mathematics:
JEE Advanced 2024 Question Paper PDF with Solutions
| Paper Name | Question Paper Link | Solutions Link |
|---|---|---|
| JEE Advanced 2024 Paper 1 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 2 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
JEE Advanced Last 5 Year Mathematics Papers Pdf
Download free JEE Advanced Previous Year Question Paper PDFs from the table provided below:-
| JEE Advanced Paper Name | Question Paper Link |
|---|---|
| JEE Advanced 2024 Question Paper PDF | Click Here |
| JEE Advanced 2023 Question Paper PDF | Click Here |
| JEE Advanced 2022 Question Paper PDF | Click Here |
| JEE Advanced 2021 Question Paper PDF | Click Here |
| JEE Advanced 2020 Question Paper PDF | Click Here |
| JEE Advanced 2019 Question Paper PDF | Click Here |
| JEE Advanced 2018 Question Paper PDF | Click Here |
| JEE Advanced 2017 Question Paper PDF | Click Here |
| JEE Advanced 2016 Question Paper PDF | Click Here |
JEE Advanced 2023 Question Paper PDF Download With Solutions
| Paper | Question Paper PDF | Answer Key PDF |
|---|---|---|
| Question Paper 1 PDF | Download PDF | Check Solutions |
| Question Paper 2 PDF | Download PDF | Check Solutions |
| Question Paper AAT PDF | Download PDF | Check Solutions |
JEE Advanced 2022 Question Paper
| 2022 Question Paper | PDF Download |
|---|---|
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
JEE Advanced 2021 Question Paper
| Question Paper | PDF Download | ||
|---|---|---|---|
| Question Paper 1 PDF | Physics | Chemistry | Maths |
| Question Paper 2 PDF | Physics | Chemistry | Maths |
JEE Advanced 2020 Question Paper
| Question Paper | PDF Download |
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
Frequently Asked Questions
Q1. Is statistics a branch of probability?
Statistics and probability are related fields in mathematics but have different applications. Probability involves predicting future events, while statistics is not a branch of probability there are some differences.
Q2. Who is the father of probability?
Pierre-Simon Laplace and Blaise Pascal are considered fathers of probability for their contribution to the development of probability theory. Laplace is known for his work on solving gambling problems, laying the groundwork for modern probability theory. Pascal’s triangle system introduced a method for calculating combinations and probabilities.
Q3. What rank is 100 marks in JEE Advanced?
100 marks rank in JEE Advanced 2025 is based on the difficulty of the exam and cutoff trends.
Expected Rank (Based on Last Year Trends) :
100-110 marks → 15,000 - 18,000 rank
120-130 marks → 10,000 - 12,000 rank
150+ marks → Less than 5,000 rank
Note: The rank is updated annually, so use maximum accuracy with no negative marking.
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