GATE Mathematics Foundation: Probability and Statistics – Previous Year Questions
12 GATE previous year questions on Probability and Statistics (Mathematics Foundation, Environmental Science and Engineering) with answers and explanations, from every paper.
- GATE 2021 ES Q37 – A biased die has faces k=1,…,6 with P(k) proportional to k². Find probability of an even result.
- GATE 2022 ES Q11 – Arsenic concentrations (mg/L) are .10,.12,.20,.05,.40,.30,.35. Which describes their distribution?
- GATE 2022 ES Q12 – A normal population yields sample25.8,36.6,26.3,21.8,27.2. Given one-sided t critical value2.132 at 5% significance with 4 degrees of freedom, select…
- GATE 2022 ES Q53 – Emails arrive60% corporate,30% Gmail,5% Yahoo,5% Zoho. Spam fractions are1%,2%,3%,3% respectively, with the same spam filter. Find probability a…
- GATE 2023 ES Q30 – Disease prevalence is .002. A test is positive with probability.98 given disease and .03 given no disease. Find probability of disease given a…
- GATE 2023 ES Q36 – Nine independent normal holding times have mean8.33 and standard deviation4.472. Sample mean M is normal. For the printed hypotheses…
- GATE 2024 ES Q11 – Ten cards are numbered1–10. Find the probability of drawing an even number or a multiple of 5.
- GATE 2024 ES Q36 – Ten observations are drawn from a normal population with mean µ. Their mean is x and standard deviation S. The supplied Student-t table lists rows…
- GATE 2025 ES Q24 – Consider (i) Pollutant concentrations are generally modeled as lognormal;(ii) concentrations are generally Poisson;(iii) weekly exceedance frequency…
- GATE 2026 ES Q14 – One card is selected randomly from 26 cards bearing the English alphabet, one distinct letter per card. What is the probability that the letter is E…
- GATE 2026 ES Q15 – Which expression is Pearson’s chi-square statistic? Here O i,E i are observed and expected frequencies,n is the number of observations, O and are the…
- GATE 2026 ES Q48 – PM concentrations at seven locations are 45,40,55,65,60,35,50 µg/m³. Find their standard deviation in µg/m³,to one decimal place.