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Topic

Probability

Asked 12 times across 3 UPSC exams over 11 years (2015–2026), peaking in 2026.
12
PYQs
3
Exams
7
Years active
2015–2026
Span
2026
Peak
6/12
Answers
📅 Full chronological timeline →

Key insights

  • Most tested in ESE — 7 of 12 PYQs
  • Most asked in 2026
  • Recurs across 7 years (2015–2026)

How it travelled across exams

First appearance in each exam — the same idea, reframed.
EPFO 2015 CAPF 2016 ESE 2022

How the concept evolved

115
116
222
123
124
125
526
Rising — more than half its appearances (11 of 12) are since 2016.

Sample questions

You've seen the pattern — here are a few of the actual PYQs.
ESE2026
What is the expectation of the number of failures preceding the first success in an infinite series of independent trials with constant probability p of success in each trial ?
  1. A q/p²
  2. B q/p
  3. C q/(1+p)
  4. D 1/(1−q)
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
A deck of n numbered cards is thoroughly shuffled and the cards are inserted into n numbered cells one by one. If the card number i falls in the cell i, we count it as a match, otherwise not, then what is the variance of total number of such matches ?
  1. A 1
  2. B 0
  3. C 1/2
  4. D 3/4
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
Let X1 and X2 be two independent random variables having variances k and 4 respectively. If the variance of Y = 3X2 − X1 is 49, then what is the value of k ?
  1. A 7
  2. B 13
  3. C 9
  4. D 11
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General

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