JEE Main · Maths · Probability

Conditional Probability: JEE Main previous year questions

Name: Conditional Probability: JEE Main previous year questions
Creator: Lumi

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

Questions: 30; in 29 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: 0.2 a shift on average, typically 0.1–0.4

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 29 of 108 shifts: 30 questions, #110 of 196 topics.
02
80% of its questions since 2020 tested an idea no earlier year had asked; 5 repeated an idea from the year before.
03
The most repeated idea is Independence Criterion, asked 5 times in 5 shifts (2021, 2022, 2024), most often as “probability of ordered draws with replacement”.
04
JEE Main has asked 18 of the 61 ideas in this topic; 39 have never been asked, directly or inside another question.
05
Mostly asked as single correct (73%); 23% need a numerical answer, 33% are easy and 10% hard.
06
The skill tested most is application (37%), then calculation (33%).

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: 5 in 12 shifts · 2021: 11 in 24 shifts · 2022: 5 in 24 shifts · 2023: 2 in 12 shifts · 2024: 3 in 18 shifts · 2025: 1 in 8 shifts · 2026: 3 in 9 shifts.

Up to 2023: 0.2; a shift, of 25
Since 2024: 0.2; 0.0
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 29/108; 27% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 30 questions on Conditional Probability since 2017.

Difficulty

QUESTIONS

10173

Easy10 · 33%
Medium17 · 57%
Hard3 · 10%

Format

Single correct · 22 Q73%
Numerical value · 7 Q23%
Two statements · 1 Q3%

Skill tested

Application · 11 Q37%
Calculation · 10 Q33%
Multi-step · 9 Q30%

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 18 of the 61 ideas in this topic. 39 have never been asked yet.

1839

Asked directly18 · 30%
Touched inside another question4 · 7%
Never asked39 · 64%

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

OpenRepeated5 · 17%17%2/823
- 25 Jul ’22 S2 · Q8
  If $A$ and $B$ are two events such that $P(A)=\frac{1}{3},P(B)=\frac{1}{5}$ and $P(A\cup B)=\frac{1}{2}$ , then $P(A|B')+P(B|A')$ is equal to
  easySingle correctAsked the year before
- 28 Jul ’22 S1 · Q9
  Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is…
  easySingle correctAsked the year before
- 24 Jun ’22 S2 · Q12
  A random variable $X$ has the following probability distribution: | $X$ | 0 | 1 | 2 | 3 | 4 | | $P(X)$ | $k$ | $2k$ | $4k$ | $6k$ | $8k$ |…
  easySingle correctAsked the year before
- 26 Aug ’21 S2 · Q78
  A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability…
  mediumSingle correctNew idea
- 31 Aug ’21 S1 · Q88
  An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that…
  mediumNumerical valueNew idea
OpenRepeated5 · 17%17%3/83
OpenRepeated3 · 10%10%2/82
Open2 · 7%7%1/82
Open2 · 7%7%1/82
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%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

18 different ideas were tested; 5 came more than once.

Independence Criterion5×
probability of ordered draws with replacement
Single correct · 5 shifts · 2 numerical
Conditional Probability Definition5×
probability from percentage data
Single correct · 5 shifts · 1 numerical
Conditional Probability in Infinite Games3×
probability of event in even-numbered trial
Numerical value · 3 shifts · 2 numerical
Multiplication Rule of Probability2×
probability of pattern in binary string
Single correct · 2 shifts
Reduced Sample Space Method2×
conditional probability for two dice throws
Numerical value · 2 shifts · 1 numerical
Bayes' Theorem with Partial String Evidence1×
bayes with partial word evidence
Single correct · 1 shift
Drawing Without Replacement1×
probability of paired draws without replacement
Single correct · 1 shift
Law of Total Probability1×
total probability over two cases
Single correct · 1 shift
Conditioning on a Union of Events1×
conditional probability given union with complement
Single correct · 1 shift
Memoryless Property in Discrete Trials1×
probability of tosses until first success
Numerical value · 1 shift · 1 numerical
Conditional Probability with De Morgan's Laws1×
truth of statements on event probabilities
Two statements · 1 shift
Conditional Probability in Infinite Games1×
probability in alternating-turn game
Single correct · 1 shift
Conditioning on Dice Sums1×
probability of dice sum with biased die
Single correct · 1 shift
Conditional Prob via Venn Diagrams1×
probability of both events from union and exactly-one
Single correct · 1 shift
Conditional Probability in Infinite Games1×
probability of winning alternating dice game
Single correct · 1 shift
Conditioning on a Complementary Event1×
true statement on independent events
Single correct · 1 shift
Conditioning on Dice Sums1×
conditional probability from dice sums
Single correct · 1 shift
De Morgan's Laws in Conditional Spaces1×
conditional probability of complements of independent events
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Independence Criterionprobability of ordered draws with replacement	5	5	Single correctApplication	2
Conditional Probability Definitionprobability from percentage data	5	5	Single correctCalculation	1
Conditional Probability in Infinite Gamesprobability of event in even-numbered trial	3	3	Numerical valueMulti-step	2
Multiplication Rule of Probabilityprobability of pattern in binary string	2	2	Single correctApplication	–
Reduced Sample Space Methodconditional probability for two dice throws	2	2	Numerical valueCalculation	1
Bayes' Theorem with Partial String Evidencebayes with partial word evidence	1	1	Single correctApplication	–
Drawing Without Replacementprobability of paired draws without replacement	1	1	Single correctMulti-step	–
Law of Total Probabilitytotal probability over two cases	1	1	Single correctApplication	–
Conditioning on a Union of Eventsconditional probability given union with complement	1	1	Single correctCalculation	–
Memoryless Property in Discrete Trialsprobability of tosses until first success	1	1	Numerical valueCalculation	1
Conditional Probability with De Morgan's Lawstruth of statements on event probabilities	1	1	Two statementsCalculation	–
Conditional Probability in Infinite Gamesprobability in alternating-turn game	1	1	Single correctMulti-step	–
Conditioning on Dice Sumsprobability of dice sum with biased die	1	1	Single correctMulti-step	–
Conditional Prob via Venn Diagramsprobability of both events from union and exactly-one	1	1	Single correctApplication	–
Conditional Probability in Infinite Gamesprobability of winning alternating dice game	1	1	Single correctMulti-step	–
Conditioning on a Complementary Eventtrue statement on independent events	1	1	Single correctApplication	–
Conditioning on Dice Sumsconditional probability from dice sums	1	1	Single correctApplication	–
De Morgan's Laws in Conditional Spacesconditional probability of complements of independent events	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

Conditional Probability 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

Conditional Probability questions, year by year

JEE Main 20263 questions in 3 shifts

JEE Main 20251 question in 1 shift

JEE Main 20243 questions in 3 shifts

JEE Main 20232 questions in 2 shifts

JEE Main 20225 questions in 5 shifts

JEE Main 202111 questions in 10 shifts

JEE Main 20205 questions in 5 shifts

More topics in Probability