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For a Binomial distribution, mean is \(15\) and variance is \(6\). If \[ P(X\ge2) = 1-\left(\frac25\right)^{25}k, \] then \(k=\)

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For Binomial distribution: \[ np=\text{Mean}, \qquad npq=\text{Variance}. \] To calculate \(P(X\ge2)\), it is often easier to use the complement: \[ P(X\ge2)=1-[P(X=0)+P(X=1)]. \]

Updated On: Jun 25, 2026

\(2^{24}\)
\(\dfrac{77}{2}\)
\(\left(\dfrac25\right)^{24}\)
\(\dfrac{78}{5}\)

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The Correct Option is B

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For a Binomial distribution, mean is \(15\) and variance is \(6\). If \[ P(X\ge2) = 1-\left(\frac25\right)^{25}k, \] then \(k=\)

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The Correct Option is B

Solution and Explanation

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