Question

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?

Answer 1

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