JEE Main · Maths · Probability

Bayes' Theorem: JEE Main previous year questions

Name: Bayes' Theorem: JEE Main previous year questions
Creator: Lumi

17 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 10 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 17; in 17 of 108 shifts
Years asked: 7/8; last asked 2026
Chance in a shift: 19%; calibrated model, how we compute it
Weighted estimate: 0.2; model; history: 0.1 a shift on average, typically 0.1–0.2

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 17 of 108 shifts: 17 questions, #150 of 196 topics.
02
35% of its questions since 2020 tested an idea no earlier year had asked; 8 repeated an idea from the year before.
03
The most repeated idea is Bayes' Theorem Application, asked 9 times in 9 shifts (2021, 2022, 2023, 2024, 2025, 2026), most often as “posterior probability by bayes theorem”.
04
JEE Main has asked 6 of the 55 ideas in this topic; 48 have never been asked, directly or inside another question.
05
Mostly asked as single correct (94%); 6% need a numerical answer, 47% are easy and 0% hard. It went up from 0.1 to 0.3 questions a shift since 2024.
06
The skill tested most is calculation (53%), then multi-step (41%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 2 in 12 shifts · 2024: 5 in 18 shifts · 2025: 3 in 8 shifts · 2026: 2 in 9 shifts.

Up to 2023: 0.1; a shift, of 25
Since 2024: 0.3; 0.2
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 17/108; 16% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 17 questions on Bayes' Theorem since 2017.

Difficulty

QUESTIONS

Easy8 · 47%
Medium9 · 53%
Hard0 · 0%

Format

Single correct · 16 Q94%
Numerical value · 1 Q6%

Skill tested

Calculation · 9 Q53%
Multi-step · 7 Q41%
Application · 1 Q6%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 6 of the 55 ideas in this topic. 48 have never been asked yet.

648

Asked directly6 · 11%
Touched inside another question1 · 2%
Never asked48 · 87%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Idea, year, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

ideaAskedShareYears’17’20’21’22’23’24’25’26

OpenRepeated9 · 53%53%6/84
- 8 Apr ’26 S2 · Q6
  A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the…
  easySingle correctAsked the year before
- 2 Apr ’25 S2 · Q9
  Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5 Bag II: Red 4, Blue 3,…
  easySingle correctAsked the year before
- 4 Apr ’24 S1 · Q19
  Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random…
  easySingle correctAsked the year before
- 6 Apr ’24 S1 · Q20
  A company has two plants $A$ and $B$ to manufacture motorcycles. $60\%$ motorcycles are manufactured at plant $A$ and the remaining are…
  easySingle correctAsked the year before
- 8 Apr ’24 S2 · Q19
  There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5…
  easySingle correctAsked the year before
- 30 Jan ’24 S2 · Q20
  Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it.…
  easySingle correctAsked the year before
- 8 Apr ’23 S1 · Q18
  In a bolt factory, machines $A$ , $B$ and $C$ manufacture respectively 20%, 30% and 50% of the total bolts. Of their output 3, 4 and 2…
  easySingle correctAsked the year before
- 24 Jun ’22 S1 · Q4
  Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2…
  mediumSingle correctAsked the year before
- 25 Feb ’21 S2 · Q75
  In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and…
  mediumSingle correctNew idea
OpenRepeated3 · 18%18%3/8
OpenRepeated2 · 12%12%2/8
Open1 · 6%6%1/8
Open1 · 6%6%1/8
Open1 · 6%6%1/8

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

6 different ideas were tested; 3 came more than once.

Bayes' Theorem Application9×
posterior probability by bayes theorem
Single correct · 9 shifts
Theorem of Total Probability3×
total probability with biased coin
Single correct · 3 shifts
Implicit Equally Likely Priors2×
probability of composition given sample drawn
Single correct · 2 shifts
Biased vs Unbiased Instrument Selection1×
probability coin was fair given head
Single correct · 1 shift
Missing or Lost Card Scenarios1×
find n from posterior of lost card
Numerical value · 1 shift · 1 numerical
Urn and Ball Transfer Problems1×
bayes with urn transfer
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Bayes' Theorem Applicationposterior probability by bayes theorem	9	9	Single correctCalculation	–
Theorem of Total Probabilitytotal probability with biased coin	3	3	Single correctMulti-step	–
Implicit Equally Likely Priorsprobability of composition given sample drawn	2	2	Single correctMulti-step	–
Biased vs Unbiased Instrument Selectionprobability coin was fair given head	1	1	Single correctCalculation	–
Missing or Lost Card Scenariosfind n from posterior of lost card	1	1	Numerical valueMulti-step	1
Urn and Ball Transfer Problemsbayes with urn transfer	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Bayes' Theorem questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Idea, year, question

Every idea inside this topic

Bayes' Theorem questions, year by year

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