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Probability

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 12 times: 2021 Paper 4, 14 Jun 2022, 25 Jan 2023, 8 Apr 2023, 30 Jan 2024, 4 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 2 Apr 2025, 5 Apr 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 12 of this type

    56
    A candidate has to go to the examination center to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 25,15\frac{2}{5},\frac{1}{5} and 25\frac{2}{5}. The probabilities that the candidate reaches late at the examination center are 15,13\frac{1}{5},\frac{1}{3} and 14\frac{1}{4} if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

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  2. Question 2

    This type asked 7 times: 28 Jul 2022, 29 Jan 2023, 5 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 7 of this type

    69
    A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is.

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  3. Question 3

    This type asked 7 times: 2021 Paper 1, 2021 Paper 10, 2021 Paper 25, 14 Jun 2022, 26 Jun 2022, 27 Jun 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 7 of this type

    158
    Let a die be rolled nn times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is k215\frac{k}{2^{15}}, then kk is equal to:

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  4. Question 4

    This type asked 6 times: 25 Jul 2022, 26 Jul 2022, 27 Jul 2022, 29 Jul 2022, 1 Feb 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 6 of this type

    164
    The random variable XX follows binomial distribution BB (n,p)(n,p) for which the difference of the mean and the variance is 1 . If 2P(X=2)=3P(X=1)2P(X = 2) = 3P(X = 1), then n2P(X>1)n^{2}P(X > 1) is equal to

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  5. Question 5

    This type asked 5 times: 2021 Paper 24, 4 Apr 2024, 7 Apr 2025, 21 Jan 2026 S2, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    54
    The probability distribution of a random variable X is given below :
    XX4k4k307k\frac{30}{7}k327k\frac{32}{7}k347k\frac{34}{7}k367k\frac{36}{7}k387k\frac{38}{7}k407k\frac{40}{7}k6k6k
    P(X)P(X)215\frac{2}{15}115\frac{1}{15}215\frac{2}{15}15\frac{1}{5}115\frac{1}{15}215\frac{2}{15}15\frac{1}{5}115\frac{1}{15}
    If E(X)=26315E(X) =\frac{263}{15}, then P(X<20)P(X< 20) is equal to :

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  6. Question 6

    This type asked 5 times: 2021 Paper 17, 6 Apr 2023, 31 Jan 2024, 4 Apr 2024, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 5 of this type

    67
    From a lot containing 10 defective and 90 nondefective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-

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  7. Question 7

    This type asked 5 times: 2021 Paper 19, 11 Apr 2023, 27 Jan 2024, 29 Jan 2024, 24 Jan 2025. This one: 24 Jan 2025 See all 5 of this type

    61
    A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8 , and BB wins if he throws a sum of 8 before AA throws a sum of 5 . The probability, that A wins if A makes the first throw, is

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  8. Question 8

    This type asked 4 times: 2021 Paper 7, 2021 Paper 20, 25 Jun 2022, 23 Jan 2025. This one: 23 Jan 2025 See all 4 of this type

    70
    One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

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  9. Question 9

    This type asked 4 times: 2021 Paper 4, 2021 Paper 6, 2021 Paper 26, 26 Jun 2022. This one: 26 Jun 2022 See all 4 of this type

    179
    If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96p96p is equal to

  10. Question 10

    This type asked 3 times: 2021 Paper 11, 25 Jul 2022, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 3 of this type

    73
    Let a,b,c∈{1,2,3,4}a,b,c \in \{ 1,2,3,4\}. If the probability, that ax2+22bx+c>0{ax}^{2} + 2\sqrt{2}bx + c > 0 for all x∈Rx \in R, is mn\frac{m}{n}, gcd(m,n)=1gcd(m,n) = 1, then m+nm + n is equal to ____\_\_\_\_ .