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Given mean and variance of a binomial: find n and p, then a probability

This type of question, asked 7 times: 3 May 2023 S2, 9 May 2023 S1, 9 May 2023 S2, 11 May 2024 S2, 11 Apr 2026 S1, 17 Apr 2026 S1, 19 May 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    109
    Let a random variable XX have a Binomial distribution with mean 8 and variance 4. If P(x≤2)=k216P(x\leq2)=\frac{k}{2^{16}}, then kk is equal to

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  2. Question 2

    9 May 2023 S1

    138
    If the mean and the variance of Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is

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  3. Question 3

    9 May 2023 S2

    142
    If the mean and the variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to

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  4. Question 4

    11 May 2024 S2

    111
    Let a random variable X have a Binomial distribution with mean 8 and variance 4. If P(X≤2)=K216P(X\leq 2) = \frac{K}{2^{16}}, then K is

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  5. Question 5

    11 Apr 2026 S1

    98
    Let X∼B(n,p)X \sim B(n, p). If E(X)=2E(X) = 2 and Var(X)=1\mathrm{Var}(X) = 1, then the probability of getting at most one success is .....

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  6. Question 6

    17 Apr 2026 S1

    99
    If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?

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  7. Question 7

    19 May 2026 S1

    99
    The sum and product of mean and variance of a binomial distribution are 3 and 2 respectively. Then, P(X>0)=…P(X > 0) = \ldots

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