JEE Main Maths · Probability PYQ

JEE Main Probability Previous Year Questions (2002–2025)

Probability (combined with Statistics) is a P1 chapter — ~5% JEE Main weightage with 1–2 questions per session. Bayes' theorem and binomial distribution are the most-repeated templates. The chapter is highly pattern-based; once you recognise the structure, solutions are mechanical.

Probability PYQs from 2002 to 2025, tagged by sub-topic (basic probability, conditional, Bayes, binomial) and difficulty. Every solution identifies the sample space and applies the correct formula explicitly.

Practise Statistics & Probability PYQs All Maths PYQs

Statistics & Probability at a Glance

Weightage

~5%

approx · 10-yr avg

Priority

Must master

Year range

2002–2025

PYQ coverage

Typical in paper

1–2

per session

Key Sub-Topics & What's Tested

Basic Probability

Sample space, events, probability of event P(A), complementary events, mutually exclusive events, classical definition.

Addition Rule

P(A ∪ B) = P(A) + P(B) - P(A ∩ B), for mutually exclusive P(A ∩ B) = 0, extension to three events.

Conditional Probability

P(A|B) = P(A ∩ B) / P(B), properties, independent events P(A|B) = P(A), multiplication rule.

Bayes' Theorem

P(A|B) = P(B|A)·P(A) / P(B), total probability theorem, classic drug-test / disease-diagnosis problem templates.

Binomial Distribution

P(X = k) = C(n,k)·p^k·(1-p)^(n-k), mean = np, variance = np(1-p), when to use (independent trials, constant p).

Random Variables & Distributions

Discrete random variable, expectation E[X] = Σ x·P(x), variance, standard deviation, properties of E and Var.

Geometric Probability

Probability via area/length ratios, target-on-circle problems, random point in geometric region.

Statistics Basics

Mean, median, mode, variance, standard deviation formulas; relationship for grouped data, coefficient of variation.

Question Type Distribution

Question Type	Share (approx)	Example Pattern
Basic Probability Calculation	20%	From a pack of 52 cards, probability of drawing 2 kings with replacement.
Conditional Probability	20%	Given box with 3 red and 5 white balls, probability of drawing red given first was red (without replacement).
Bayes' Theorem Application	25%	Given false positive rate and base rate, find probability of disease given positive test.
Binomial Distribution	20%	Probability of exactly 3 sixes in 5 rolls of a fair die.
Expected Value	10%	Find expected number of tails in 4 coin tosses.
Geometric Probability	5%	Probability that a random point in unit square satisfies x + y ≥ 1.

How to Solve Statistics & Probability PYQs

1
Identify sample space first. Write down total outcomes explicitly. Most probability errors come from miscounting the sample space.
2
For conditional problems, set up P(A|B) = P(A ∩ B) / P(B). Figure out both the joint and marginal probabilities separately, then divide.
3
Bayes: apply total probability first. P(B) = P(B|A₁)P(A₁) + P(B|A₂)P(A₂) + ..., then divide to get P(A|B). Build a tree diagram.
4
Binomial check: independent + constant p + fixed n. If any of these fail, it's NOT binomial (might be hypergeometric or negative binomial).
5
For independence, P(A ∩ B) = P(A)·P(B). Don't assume independence — verify it. PYQs often test whether events are actually independent.

Common Mistakes That Cost Marks

Confusing 'at least one' with 'exactly one'. P(at least one) = 1 - P(none). P(exactly one) uses binomial C(n, 1)·p·(1-p)^(n-1).
Forgetting 'without replacement' vs 'with replacement'. Changes whether probabilities are constant across draws. Binomial assumes independence = with replacement.
Applying Bayes' formula backwards. P(A|B) ≠ P(B|A) in general. Always use P(A|B) = P(B|A)·P(A) / P(B).
Using permutation vs combination wrong. Probability of unordered outcomes uses combinations. Ordered (sequence matters) uses permutations. Match to problem.
Treating non-exclusive events as exclusive. P(A ∪ B) = P(A) + P(B) only if mutually exclusive. Otherwise subtract intersection.

JEE Main Maths PYQ Chapter-Wise

Browse PYQs across all Maths chapters.

JEE Main Permutations & Combinations PYQ

Prerequisite — counts the sample space for probability.

JEE Main Matrices & Determinants PYQ

Algebra partner chapter — ~6% weightage.

Top High-Weightage Maths Chapters (data-backed)

Where Probability sits in the priority order.

JEE Main Maths Syllabus with Priority Tiers

Full Maths syllabus with priority tiers.

JEE Main Rank Predictor

Convert a target percentile into an expected rank.

Frequently asked questions

How many Probability PYQs should I solve?

Target 50–70 PYQs across 2010–2025. Given high template repeat (Bayes, binomial, conditional), focused practice reaches strong accuracy quickly.

Is Bayes' theorem heavily tested in JEE Main?

Yes — 3–4 Bayes PYQs per 10-year window. Usually as classic drug-test / weather-forecast / two-urn probability problems. Master the tree-diagram approach.

Do I need measure theory or advanced probability?

No — JEE Main stays with basic probability, conditional, Bayes and binomial. Advanced topics (continuous distributions, moments) are beyond the syllabus.

What's the most-tested Probability PYQ template?

Bayes with two/three conditions — e.g., two urns with different colour ratios, draw a ball, find probability it came from urn 1 given it's red. Classic template, 3–4 variants per decade.

Should I memorise binomial mean and variance?

Yes — mean = np, variance = np(1-p) for binomial. These appear in standalone PYQs ('find variance of X' type) at least once per paper when binomial is tested.

Are statistics PYQs tested separately?

Yes — 1 statistics PYQ per paper typically. Mean, median, mode, variance, standard deviation. Less deep than probability but still requires formula recall.

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