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In a binomial distribution B(n,p=1/4),If the probability of atleast one success is greater that or equal to 9/10 then nis greater than?



X denotes here number of success (random varaiable X)
it is binomial distribution
p=1/4 and q=1/4
P(X=1)= \frac{n!}{(n-1)!1!} \frac{1}{4}  (\frac{3}{4})^{n-1} \geq  \frac{9}{10}
n \frac{1}{3}  (\frac{3}{4})^{n} \geq  \frac{9}{10}
n  (\frac{3^n}{4^n}) \geq  \frac{3^3}{10}
so for statement no value of n is possible such that it is greater than 2.7

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