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Mean or variance of the number of successes using np and npq

This type of question, asked 9 times: May 2022 S1, 3 May 2023 S2, 11 May 2023 S1, 16 May 2023 S1, 9 May 2024 S1, 9 May 2024 S2, 11 May 2024 S2, 21 Apr 2025 S2, 15 Apr 2026 S1. All 9 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    136
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

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  2. Question 2

    3 May 2023 S2

    150
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

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  3. Question 3

    11 May 2023 S1

    119
    If three fair coins are tossed, then variance of number of heads obtained, is

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  4. Question 4

    16 May 2023 S1

    150
    A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one by one, with replacement, then the variance of the number of green balls drawn is

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  5. Question 5

    9 May 2024 S1

    133
    Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var(X) of the probability distribution of random variable X, where X is the sum of numbers on the uppermost faces, is

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  6. Question 6

    9 May 2024 S2

    146
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards, then mean of number of queens is

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  7. Question 7

    11 May 2024 S2

    142
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of tens is

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  8. Question 8

    21 Apr 2025 S2

    119
    A random variable X has p.m.f. P(X=x)= 4Cx24,x=0,1,2,3,4P(X =x) =\frac{\ ^{4}C_{x}}{2^{4}},x= 0,1,2,3,4 and μ\mu and σ2\sigma^{2} are mean and variance respectively of random variable X , then

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  9. Question 9

    15 Apr 2026 S1

    99
    The Variance of the following probability distribution of X is
    X00112233
    P(X)q3q^33q2p3q^2p3qp23qp^2p3p^3
    where 0<p<1,q=1−p0 < p < 1, q = 1 - p

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