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The mean and variance of a random variable $\mathrm{X}$ having binomial distribution are 4 and 2 respectively, then $\mathrm{P}(\mathrm{X}=1)$ is
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$\frac{1}{32}$
$\begin{aligned} n p &=4 \\ n p q &=2 \\ \Rightarrow q &=\frac{1}{2}, p=\frac{1}{2}, n=8 \\ \mathrm{P}(\mathrm{X}&=1)={ }^{8} \mathrm{C}_{1}\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)^{7}=8 \cdot \frac{1}{2^{8}}=\frac{1}{2^{5}}=\frac{1}{32} \end{aligned}$
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