A) \[\frac{1}{\log _{10}^{4}-\log _{10}^{3}}\]
B) \[\frac{1}{\log _{10}^{4}+\log _{10}^{3}}\]
C) \[\frac{9}{\log _{10}^{4}-\log _{10}^{3}}\]
D) \[\frac{4}{\log _{10}^{4}-\log _{10}^{3}}\]
Correct Answer: A
Solution :
\[P(x\ge 1)\ge \frac{9}{10}\] \[\Rightarrow \] \[1-P(x=0)\le \frac{9}{10}\] \[\Rightarrow \] \[\frac{1}{10}\ge {{\left( \frac{3}{4} \right)}^{n}}\] \[\Rightarrow \] \[{{\left( \frac{3}{4} \right)}^{n}}\le \frac{1}{10}\] \[\Rightarrow \] \[n[\log _{10}^{3}-\log _{10}^{4}]\le -1\] \[\Rightarrow \] \[n\ge \frac{1}{\log _{10}^{4}-\log _{10}^{3}}\]
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