A) \[\frac{1}{16}\]
B) \[\frac{3}{16}\]
C) \[\frac{5}{16}\]
D) \[\frac{15}{16}\]
Correct Answer: D
Solution :
Given mean, \[np=2\] and variance, \[npq=1\] \[\therefore \] \[2(q)\,=2\,\,\Rightarrow q=\frac{1}{2}\] \[\Rightarrow \] \[p=\frac{1}{2}\] and \[n=4\] \[\therefore \] \[P(X\ge 1)=1-P(X=0)\] \[=1{{-}^{4}}{{C}_{0}}{{\left( \frac{1}{2} \right)}^{0}}{{\left( \frac{1}{2} \right)}^{4}}\] \[=1-1\times \frac{1}{16}=\frac{15}{16}\]
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