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Binomial with mean 2 and variance 1: probability X is above or below 1

The same question, asked 3 times: 9 May 2023 S1*, 9 May 2023 S2*, 11 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    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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  2. Question 2

    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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  3. Question 3

    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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