In Binomial distribution, if $E(X)=40 $ and $V(X)=8, $ then value of $P(X=1), $ is :

$\frac{8}{5^{48}}$

The correct answer is Option (1) → $\frac{8}{5^{48}}$

In a Binomial Distribution,

Mean = $E(X)=np=40$ [Given]   ...(1)

Variance = $V(X)=np(1-p)=8$ [Given]   ...(2)

Substituting $np=40$ in equation (2)

$40(1-p)=8$

$1-p=\frac{1}{5}$

$p=\frac{4}{5}$

$⇒n=40×\frac{5}{4}=50$

$P(X+1)={^{50}C}_1(\frac{4}{5})(\frac{1}{5})^{49}$

$=\frac{8}{5^{48}}$