If the mean and the variance of a binomial variate 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. `15//16`

Answer

D

Explanation

Let n and p be the parameters of the binomial distribution. Then,
`np=2 and npq=1`
`rArr q=(1)/(2),p=(1)/(2)and n=4 " "["Given"]`
`therefore P(Xge 1)=1-P(Xlt1)=1-P(X=0)`
`rArr P(Xge1)-.^Nc_(0)p^(0)q^(n-0)=1-.^4C_(0)xx((1)/(2))^4=(15)/(16)`