If a random variable X follows Binomial distribution with mean 8 and variance 4, then P(X> 1) is :

$\frac{65535}{65536}$

The correct answer is Option (3) → $\frac{65535}{65536}$

The Binomial probability mass function

$P(X=x)={^nC}_xp^x(1-p)^{n-x}$

$P(X≤x)=P(X=0)+P(X=1)$

$=(0.05)^{16}+16(0.5)^{16}=17(0.5)^{16}$

$∴P(X>1)=1-17(0.5)^{16}=\frac{65535}{65536}$