$\begin {array} {1 1} (A)\;\large\frac{1}{6} & \quad (B)\;\large\frac{5}{16} \\ (C)\;\large\frac{11}{16} & \quad (D)\;\large\frac{15}{16} \end {array}$

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$ np=2$

$ n\: pq=1$

$ Q= \large\frac{1}{2}$

$ n = 4$

$P=\large\frac{1}{2}$

$ \therefore $ Required probability = $ P( X > 1)$

$ 1-P ( X \leq 1 )$

$ = 1-[P(0)+P(1)]$

$ = 1- \bigg[ 4C_0 \bigg( \large\frac{1}{2} \bigg)^4+4C_1 \bigg( \large\frac{1}{2} \bigg)^3 \bigg( \large\frac{1}{2} \bigg) \bigg]$

$ = \large\frac{11}{16}$

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