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Probability Distribution

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET 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 9 times: May 2021 S1, 2 May 2023 S2, 3 May 2023 S2, 4 May 2023 S2, 9 May 2023 S1, 26 Apr 2025 S2, 15 Apr 2026 S2, 20 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 9 of this type

    99
    The variance of randam variable XX, for the following probability mass function (p. m. f.) is ...
    X=xX = x112233
    P(X=x)P(X = x)15\dfrac{1}{5}25\dfrac{2}{5}25\dfrac{2}{5}

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  2. Question 2

    This type asked 8 times: 20 Apr 2025 S2, 23 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    100
    A man is known to speak the truth in 75%75\% of cases. If he throws an unbiased die and tells his friend that it is a six. Assuming that when he tells a lie, he specifically reports the result as a six, the probability that it is actually a six is...

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  3. Question 3

    This type asked 7 times: 4 May 2023 S2, 9 May 2023 S2, 16 May 2023 S1, 16 May 2023 S2, 9 May 2024 S2, 22 Apr 2025 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 7 of this type

    100
    A husband and wife appeared for an interview for two vacancies in an office. The probability of the husband's selection is 15\dfrac{1}{5} and that of the wife's selection is 17\dfrac{1}{7}, then the probability that exactly one of them is selected is...

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  4. Question 4

    Asked 6 times: 10 May 2023 S1*, 11 May 2023 S2*, 13 May 2024 S2*, 13 Apr 2026 S1*, 15 Apr 2026 S2*, 16 Apr 2026 S1 (* = numbers or wording changed that year) See all 6 times it was asked

    98
    A random variable X has the probability distribution
    X=xX = x12345678
    P(X=x)P(X = x)0.230.150.120.100.200.070.080.05
    for the events E = {X is a prime number} and F = {X ≤\le 3}, then P (E∪\cupF)=

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  5. Question 5

    This type asked 6 times: 4 May 2023 S1, 15 May 2023 S1, 16 May 2023 S1, 25 Apr 2025 S1, 25 Apr 2025 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 6 of this type

    99
    The probability mass function (p.m.f.) of a random variable X is as follows: P(X=0)=3k3, P(X=1)=4k−10k2, P(X=2)=5k−1, P(X=x)=0P(X = 0) = 3k^3,\ P(X = 1) = 4k - 10k^2,\ P(X = 2) = 5k - 1,\ P(X = x) = 0 for any value of xx, then the value of kk is:

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  6. Question 6

    This type asked 6 times: 3 May 2023 S1, 10 May 2023 S1, 10 May 2024 S2, 19 Apr 2025 S2, 23 Apr 2025 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 6 of this type

    100
    Consider a game of tossing a six sided fair die. If the face that comes up is 66, the player wins Rs. 3636 and he loses Rs. k2k^2, where kk is the face that comes up k={1,2,3,4,5}k = \{1, 2, 3, 4, 5\}, then the expected winning amount in this game in Rs. is...

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  7. Question 7

    This type asked 5 times: 3 May 2023 S1, 19 Apr 2025 S1, 20 Apr 2025 S1, 25 Apr 2025 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    99
    The probability distribution of a discrete random variable (r.v.) XX is given below:
    X=xX = x0011223344
    P(X=x)P(X = x)kk2k2k4k4k2k2kkk
    Then the value of P[X≤E(X)]P[X \le E(X)] is:

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  8. Question 8

    This type asked 5 times: 14 May 2024 S1, 22 Apr 2025 S1, 20 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 5 of this type

    99
    Let X be a random variable with the probability density function defined by f(x)=1x2,1<x<∞f(x) = \dfrac{1}{x^2}, 1 < x < \infty =0= 0 otherwise. If C1={x:1<x<2}C_1 = \{x : 1 < x < 2\} and C2={x:4<x<5}C_2 = \{x : 4 < x < 5\} then P(C1∪C2)=P(C_1 \cup C_2) =

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  9. Question 9

    This type asked 5 times: 2 May 2023 S1, 11 May 2023 S2, 16 May 2023 S2, 20 Apr 2025 S2, 21 Apr 2025 S1. This one: 21 Apr 2025 S1 See all 5 of this type

    111
    A random variable X takes values 0,1,2,30,1,2,3, ____\_\_\_\_ with probabilities. P(X=x)=k(x+1)(12)x,kP(X =x) = k(x+ 1)\left( \frac{1}{2} \right)^{x},k is a constant, then P(X=1)=P(X= 1) =

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  10. Question 10

    Asked 4 times: 2 May 2023 S1, 11 May 2023 S2, 16 May 2023 S2, 20 Apr 2025 S2 See all 4 times it was asked

    145
    A random variable X takes the values 0, 1, 2, 3, ____\_\_\_\_ with probability P(X=x)=k(x+1)(15)xP(X =x) = k(x+ 1)\left( \frac{1}{5} \right)^{x}, where k is a constant.Then P(X=0)P(X = 0) is

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