If a random variable X follows Binomial distribution with mean 8 and variance 4, then P(X> 1) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{65535}{65536}$
The Binomial probability mass function
$P(X=x)={^nC}_xp^x(1-p)^{n-x}$
$P(X≤x)=P(X=0)+P(X=1)$
$=(0.05)^{16}+16(0.5)^{16}=17(0.5)^{16}$
$∴P(X>1)=1-17(0.5)^{16}=\frac{65535}{65536}$