Probability — JEE Main Previous Year Questions

How many JEE Main questions come from Probability?

Probability has contributed 181 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 16 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 181 questions carries a written, step-by-step solution, and each is tagged to Probability within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Probability questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 181 Probability questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2026

   From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is
   1. (A)$\frac{73}{10^8}$
   2. (B)$\frac{67}{10^8}$
   3. (C)$\frac{7}{10^7}$
   4. (D)$\frac{81}{10^8}$
   Show answerAnswer

   Answer: (A) $\frac{73}{10^8}$

2. Question 2 · JEE Main 2026

   A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :
   1. (A)$\frac{63}{925}$
   2. (B)$\frac{17}{231}$
   3. (C)$\frac{16}{231}$
   4. (D)$\frac{64}{925}$
   Show answerAnswer

   Answer: (C) $\frac{16}{231}$

3. Question 3 · JEE Main 2026

   A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:
   1. (A)$\frac{7}{10}$
   2. (B)$\frac{10}{17}$
   3. (C)$\frac{12}{19}$
   4. (D)$\frac{7}{19}$
   Show answerAnswer

   Answer: (B) $\frac{10}{17}$

4. Question 4 · JEE Main 2025

   Let a random variable X take values 0, 1, 2, 3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3)=q and E(X^2)=2E(X). Then the value of 8p−1 is :
   1. (A)2
   2. (B)0
   3. (C)3
   4. (D)1
   Show answerAnswer

   Answer: (A) 2

5. Question 5 · JEE Main 2025

   The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is
   1. (A)$\frac{129}{182}$
   2. (B)$\frac{17}{26}$
   3. (C)$\frac{19}{26}$
   4. (D)$\frac{103}{182}$
   Show answerAnswer

   Answer: (A) $\frac{129}{182}$

Probability questions by year

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