A) \[1/4\]
B) \[1/16\]
C) \[1/8\]
D) \[1/32\]
Correct Answer: D
Solution :
Given, mean, \[np=4\] ?.(i) Variance, \[npq=2\] ?.(ii) \[\frac{npq}{np}=\frac{2}{4}\] \[\Rightarrow \] \[q=\frac{1}{2}\] \[\therefore \] \[p=\frac{1}{2}\] From Eq (i), we get \[n=\frac{4}{1/2}=8\] Now, \[P(X=1){{=}^{n}}{{C}_{1}}{{p}^{1}}{{q}^{n-1}}\] \[{{=}^{8}}C & {{ & }_{1}}{{\left( \frac{1}{2} \right)}^{1}}{{\left( \frac{1}{2} \right)}^{7}}=\frac{8!}{1!7!}\times \frac{1}{{{2}^{8}}}=\frac{8}{{{2}^{8}}}=\frac{1}{32}\]
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