Probability & Statistics for GATE DA: The Heaviest Section, Mastered
The GATE DA section that carried the most marks in 2024–2026 — every past question indexed, the distributions and formulas that recur, seven worked numericals, and a topic tracker.
Updated : 15 hours ago
View Complete ArticleChecked 25 September 2026. Syllabus and past-paper data are official and fixed. Formulas are standard statistics.
Probability & Statistics is Section 1 of the GATE DA syllabus and, in our question-by-question count of the three official papers, the section that carried the most marks over the three years: 15 in 2024, 19 in 2025 and 21 in 2026, out of 85 subject marks per paper (100 including General Aptitude). It also sits underneath two other sections — naive Bayes, LDA and regression in Machine Learning, and conditional independence and inference in AI — so time spent here pays twice.
From the official answer keys, classified by us. 2024: 3 MCQ, 0 MSQ, 6 NAT; 2025: 9 MCQ, 1 MSQ, 2 NAT; 2026: 4 MCQ, 3 MSQ, 6 NAT.
| 2024 | 2025 | 2026 | Section (our count) | Three years |
|---|---|---|---|---|
| 15 | 19 | 21 | Probability & Statistics | 55 |
| 20 | 14 | 14 | Programming, DS & Algorithms | 48 |
| 15 | 12 | 13 | Machine Learning | 40 |
| 7 | 11 | 18 | DBMS & Warehousing | 36 |
| 10 | 12 | 8 | Linear Algebra | 30 |
| 10 | 6 | 8 | AI (search, logic, uncertainty) | 24 |
| 8 | 11 | 3 | Calculus & Optimization | 22 |
Marks per section in the three papers, from our question-by-question classification — the basis for calling P&S the heaviest section. The method and the judgement calls are in our weightage guide.
The official syllabus, grouped the way it is examined
| Block | Syllabus topics |
|---|---|
| Counting and probability | Permutations and combinations; axioms; sample space and events; independent and mutually exclusive events; marginal, conditional and joint probability; Bayes theorem |
| Descriptive statistics | Mean, median, mode, standard deviation; correlation and covariance |
| Random variables | Discrete RVs and PMFs; continuous RVs and PDFs; CDFs; conditional PDF; conditional expectation and variance |
| Distributions | Uniform, Bernoulli, binomial, Poisson, exponential, normal, standard normal, t, chi-squared |
| Inference | Central limit theorem; confidence intervals; z-test, t-test, chi-squared test |
Every P&S question in the three papers
| Paper | Question numbers |
|---|---|
| GATE 2024 | 11, 12, 34, 36, 56, 57, 58, 59 (marks to all), 65 |
| GATE 2025 | 11, 19, 20, 21, 31, 36, 39, 40, 41, 45, 54, 61 |
| GATE 2026 | 19, 20, 28, 33, 34, 44, 45, 53, 54, 57, 62, 63, 64 |
Links to all three official papers and keys are in GATE DA previous year papers. Themes that came back more than once: Bayes numericals (2024 Q58, 2025 Q31, 2026 Q57); the exponential distribution — parameter and tail (2024 Q57; 2025 Q21), memorylessness (2026 Q34) and its link to the geometric (2025 Q41); conditional expectation (2024 Q59, 2025 Q11); CDFs (2025 Q19, Q39; 2026 Q54); covariance and correlation (2024 Q65, 2026 Q63); the CLT (2025 Q40, 2026 Q45); counting (2026 Q19, Q20, Q33).
The distributions, on one table
| Distribution | PMF / PDF | Mean | Variance |
|---|---|---|---|
| Bernoulli(p) | P(X=1)=p, P(X=0)=1−p | p | p(1−p) |
| Binomial(n, p) | C(n,k) pᵏ(1−p)ⁿ⁻ᵏ | np | np(1−p) |
| Poisson(λ) | e^(−λ) λᵏ / k! | λ | λ |
| Uniform(a, b) | 1/(b−a) on [a, b] | (a+b)/2 | (b−a)²/12 |
| Exponential(λ) | λe^(−λx), x ≥ 0 | 1/λ | 1/λ² |
| Normal(μ, σ²) | bell curve; Z = (X−μ)/σ | μ | σ² |
| t (ν d.f.) | heavier tails than normal | 0 (ν > 1) | ν/(ν−2) (ν > 2) |
| Chi-squared (k d.f.) | sum of k squared standard normals | k | 2k |
Five identities that do most of the work
- Bayes: P(A|B) = P(B|A)P(A) / P(B), with P(B) from the law of total probability.
- Total expectation: E[X] = E[E[X|Y]]; total variance: Var(X) = E[Var(X|Y)] + Var(E[X|Y]).
- Variance of a sum: Var(X+Y) = Var X + Var Y + 2Cov(X,Y); Cov(X,Y) = ρσₓσᵧ.
- Memorylessness: for exponential T, P(T > s+t | T > s) = P(T > t).
- CLT: the mean of n i.i.d. variables with mean μ and s.d. σ is approximately Normal(μ, σ²/n) for large n.
Two habits make these formulas pay off in the exam. Identify the distribution from the story before touching numbers — "time until the next arrival" is exponential, "number of arrivals in an hour" is Poisson, "successes in n independent trials" is binomial. And check every answer against the obvious bounds: a probability between 0 and 1, a variance that is never negative, a correlation between −1 and 1.
Seven worked numericals
Each is in the style of a GATE numerical-answer question, built to use one idea from the tables above. Try each before reading the answer.
1. Bayes
- A disease affects 1% of a population. A test detects it 95% of the time and gives a false positive 5% of the time. If a person tests positive, what is the probability they have the disease?
- P(D|+) = (0.95 × 0.01) / (0.95 × 0.01 + 0.05 × 0.99) = 0.0095 / 0.0590 = 0.161. Most positives are false because the disease is rare.
2. Memorylessness
- A component's lifetime is exponential with mean 10 hours. It has already run 5 hours. What is the probability it runs more than 10 further hours?
- P(T > 15 | T > 5) = P(T > 10) = e^(−10/10) = e^(−1) = 0.368. The 5 hours already run are irrelevant.
3. Binomial
- A fair coin is tossed 10 times. Probability of exactly 3 heads?
- C(10,3)/2¹⁰ = 120/1024 = 0.117.
4. Poisson
- Requests arrive at 2 per hour on average (Poisson). Probability of none in an hour, and of at least 2?
- P(0) = e^(−2) = 0.135. P(≥2) = 1 − e^(−2)(1 + 2) = 0.594.
5. Law of total expectation
- Roll a fair die. If it is even, toss two fair coins; if odd, toss one. Expected number of heads?
- E = ½ × 1 + ½ × ½ = 0.75.
6. Variance of a sum
- Var(X) = 4, Var(Y) = 9, correlation 0.5. Find Var(X + Y).
- Cov = 0.5 × 2 × 3 = 3, so Var(X+Y) = 4 + 9 + 2 × 3 = 19.
7. CLT and a confidence interval
- A sample of 36 from a population with σ = 6 has mean 20. Give the 95% confidence interval for μ; and if the population mean were 50 with σ = 10, what is P(mean of 100 draws > 52)?
- Standard error = 6/√36 = 1, so 20 ± 1.96 = (18.04, 21.96). For the second, the sample mean ~ Normal(50, 1), so P(X̄ > 52) = P(Z > 2) = 0.023.
Illustrative questions written for this guide, not taken from a GATE paper.
Where probability reappears in other sections
The marks above are only the questions filed under Section 1. Probability does a lot of quiet work elsewhere in the paper, which is why its effective weight is higher than its own count.
| Other section | Syllabus topic | The probability underneath |
|---|---|---|
| Machine Learning | Naive Bayes classifier | Bayes theorem plus conditional independence of features given the class |
| Machine Learning | Linear discriminant analysis | Gaussian class-conditional densities with a shared covariance |
| Machine Learning | Logistic regression | Modelling P(y = 1 | x) and maximising likelihood |
| Machine Learning | PCA | Eigen-decomposition of the covariance matrix; variance explained |
| AI | Reasoning under uncertainty | Conditional independence, exact inference by variable elimination, approximate inference by sampling |
| DBMS & Warehousing | Data transformation | Normalisation (z-scores), discretisation, sampling |
In practice this means the order of study matters: finish conditional probability, Bayes and covariance before you start naive Bayes, LDA or PCA, and the machine-learning section becomes largely an application of what you already know rather than a new subject.
Traps the past papers set
| Trap | Where it bites | Defence |
|---|---|---|
| Conditioning on the wrong event | Bayes and conditional-probability NATs | Write "given what?" in words before any formula |
| Independent vs mutually exclusive | Event-property questions | Mutually exclusive events with non-zero probability are never independent |
| PDF value read as a probability | Continuous RV questions | Probabilities of continuous RVs are areas; a PDF can exceed 1 |
| Variance of a sum without covariance | Covariance/correlation items | Add 2Cov unless independence is given |
| σ vs σ/√n | CLT and confidence intervals | The spread of a mean shrinks with √n |
| Rounding a NAT too early | Any numerical answer | Keep four figures until the last step |
Probability is best learned in short daily sets: through October, five to ten past-paper P&S questions a day — the 34 in the three official papers first — covers the section twice before November.
Practise it, don't just read it
There is no probability quiz in the library yet; use it for the linear-algebra and neural-network topics that build on this section.
The ProSyllabus GATE DA library currently has three topic quizzes: Matrix Rank and Inverse (Section 2, Linear Algebra), Backpropagation in Neural Networks (Section 6, multi-layer perceptrons) and Gradient Descent Variants (optimisation practice for Machine Learning — the syllabus names no gradient methods, though a 2026 question applied an SGD update). Each has ten questions and a worked explanation for every option. Probability, programming and DBMS have no quizzes yet — drill those from the section index of the official papers.
How much weightage does Probability and Statistics have in GATE DA?
In our question-by-question count of the official papers it carried 15 marks in 2024, 19 in 2025 and 21 in 2026, out of 85 subject marks — the most of any section in 2025 and 2026, and 55 of 255 marks across the three years.
Which probability topics are most important for GATE DA?
Topics that recurred in the official papers include Bayes theorem numericals, the exponential distribution and memorylessness, conditional expectation, CDFs, covariance and correlation, the central limit theorem and counting.
Are statistical tests in the GATE DA syllabus?
Yes. The syllabus includes confidence intervals, the z-test, the t-test and the chi-squared test, along with the central limit theorem and the t and chi-squared distributions.
Are GATE DA probability questions numerical?
Many are. Of the 34 probability and statistics questions in the 2024 to 2026 papers, 14 were numerical-answer questions, where you type the value, and 16 were MCQs, which carry negative marking.
Which book is good for GATE DA probability?
Any standard undergraduate probability and statistics text that covers the syllabus topics listed on this page will do; what matters more is solving every probability question from the three official DA papers, which show the depth GATE expects.
More in this series
- GATE DA topic-wise weightage, counted from 2024–2026 papers
- GATE DA marks vs score vs rank, with calculator
- GATE DA previous year papers 2024–2026, with answer keys
- GATE DA or GATE CS — which paper, and writing both
- GATE DA 2027 week-by-week plan, October to February
- GATE DA without a CS degree
- GATE DA cutoffs, rank vs IIT and placements
- GATE DA notice board — official updates
Sources
- official — GATE 2027 DA syllabus (IIT Madras)
- official — GATE 2024 DA question paper (IISc)
- official — GATE 2024 DA final answer key
- official — GATE 2025 DA question paper (IIT Roorkee)
- official — GATE 2025 DA answer key
- official — GATE 2026 DA question paper (IIT Guwahati)
- official — GATE 2026 DA answer key
official = a document published by the conducting body. reported = a news or coaching site we could not check against an original. Where sources disagree this page says so rather than picking one.
