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(B) For a binomial distribution, the mean is given by $np = 2$ and the variance is given by $npq = 1$. Dividing the variance by the mean, we get $\fra

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$\frac{15}{16}$

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(B) For a binomial distribution, the mean is given by $np = 2$ and the variance is given by $npq = 1$. Dividing the variance by the mean, we get $\frac{npq}{np} = \frac{1}{2}$, which implies $q = \frac{1}{2}$. Since $p + q = 1$, we have $p = 1 - \frac{1}{2} = \frac{1}{2}$. Substituting $p = \frac{1}{2}$ into $np = 2$, we get $n 	imes \frac{1}{2} = 2$, so $n = 4$. The probability mass function is $P(X = k) = \binom{n}{k} p^k q^{n-k} = \binom{4}{k} (\frac{1}{2})^k (\frac{1}{2})^{4-k} = \binom{4}{k} (\frac{1}{2})^4 = \binom{4}{k} \frac{1}{16}$. We need to find $P(X \geq 1) = 1 - P(X = 0)$. $P(X = 0) = \binom{4}{0} (\frac{1}{2})^4 = 1 	imes \frac{1}{16} = \frac{1}{16}$. Therefore, $P(X \geq 1) = 1 - \frac{1}{16} = \frac{15}{16}$.

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively, then $P(X \geq 1)$ is equal to

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