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JEE Main Probability questions with solutions

Conditional probability, Bayes theorem and distributions. 9 questions from our 2017–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Probability for JEE Advanced · Probability for CAT · Probability for NDA

JEE Main 2025

Bag I has 3 red and 2 black balls; Bag II has 2 red and 4 black balls. A fair die is thrown: if 1 or 2 appears, a ball is drawn from Bag I, otherwise…JEE Main 2025 · medium

JEE Main 2024

Given that the first die shows an odd number, the probability that the sum is 7 isJEE Main 2024 · medium
A fair die is rolled repeatedly until a six appears for the first time. The probability that the number of rolls needed is even equals p/q in lowest…JEE Main 2024 · medium

JEE Main 2023

A fair coin is tossed repeatedly until two consecutive heads appear for the first time. Given that this happens within the first 6 tosses, the…JEE Main 2023 · hard

JEE Main 2022

A pair of unbiased dice is rolled. Given that the first die shows an even face, the chance that the total is 8 equalsJEE Main 2022 · medium

JEE Main 2021

JEE Main 2019

A pair of unbiased dice is rolled once. If it is known that at least one die shows an even face, then the probability that the total of the two faces…JEE Main 2019 · medium

JEE Main 2017

When an unbiased coin is flipped five times, the chance that heads shows up in exactly three flips isJEE Main 2017 · easy

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Differentiation and Application of Derivatives 19 Indefinite and Definite Integrals 16 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8