If the mean and the variance of a binomial variable X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to:

Options

A. `(2)/(3)`
B. `(4)/(5)`
C. `(7)/(8)`
D. `(11)/(16)`

Answer

D

Explanation

We have, np=2=mean
npq=1=varance
`Rightarrow p=(1)/(2),q=(1)/(2)& n=4`
Required probability=`P(x gt 1)`
`=1-P(x lt 1)`
`=1-P(x=0)+P(x=1)`
`=1-[.^(4)C_(0)q^(4)+.^(4)C_(1)q^(3)p^(1)]`
`=1-(5)/(16)=(11)/(16)`