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# The mean and standard deviation of a binomial variate X are 4 and $\sqrt 3$ respectively. The $P( X \geq 1 )$ is equal to

$\begin {array} {1 1} (A)\;1- \bigg(\large\frac{1}{4} \bigg)^{16} & \quad (B)\;1- \bigg(\large\frac{3}{4} \bigg)^{16} \\ (C)\;1- \bigg(\large\frac{2}{3} \bigg)^{16} & \quad (D)\;1- \bigg(\large\frac{1}{3} \bigg)^{16} \end {array}$

Given :
Mean = 4
Variance = $npq = 3$
On solvng we get,
$Q=\large\frac{3}{4}$
$n = 16$
$p = \large\frac{1}{4}$
$P ( X \geq 1 ) = 1- P(x=0)$
$= 1-nC_0P^0Q^{n-0}$
$= 1- \bigg( \large\frac{3}{4} \bigg)^{16}$