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 :
[a]| Here\[p=\frac{1}{4},\]\[q=\frac{3}{4}\] |
| \[p\,(X\ge 1)=1-p\,(X=0)\] |
| \[=1-{}^{n}{{C}_{0}}{{p}^{0}}{{q}^{n}}\] |
| \[1-{{\left( \frac{3}{4} \right)}^{n}}\ge \frac{9}{10}\] \[\left[ \because p(x\ge 1)\ge \frac{9}{10} \right]\] |
| \[\Rightarrow \]\[\frac{1}{10}\ge {{\left( \frac{3}{4} \right)}^{n}}\]\[\Rightarrow \]\[10\le {{\left( \frac{4}{3} \right)}^{n}}\] |
| \[\Rightarrow \]\[n\ge \frac{1}{{{\log }_{10}}4/3}=\frac{1}{{{\log }_{10}}4-{{\log }_{10}}3}\] |
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