question_answer

In a binomial distribution \[B\left( n,p=\frac{1}{4} \right),\] if the probability of atleast one success is greater than or equal to \[\frac{9}{10},\]  then n is greater than ______.

A)  \[\frac{4}{{{\log }_{10}}4-{{\log }_{10}}3}\]   

B)  \[\frac{9}{{{\log }_{10}}4-{{\log }_{10}}3}\]

C)  \[\frac{1}{{{\log }_{10}}4+{{\log }_{10}}3}\] 

D)  \[\frac{1}{{{\log }_{10}}4-{{\log }_{10}}3}\]

E)  None of these