IF the mean and the variance of a binomial distribution are 4 and 3 respectively ,then the probability of six successes is

Options

A. `.^16C_(6)((1)/(4))^6((3)/(4))^10`
B. `.^16C_(6)((1)/(4))^16((3)/(4))^20`
C. `.^16C_(6)((1)/(4))^8((3)/(4))^12`
D. `.^16C_(9)((1)/(4))^16((3)/(4))^20`

Answer

A

Explanation

Let `X˜B(n,p)` be a binomial variate with mean 4 and variance 3. Then,
`np=4,and npq=3rArr q=(3)/(4),p=(1)/(4) and n=16`
`thereforeP(X=r)=.^16C_(r)((1)/(4))^r((3)/(4))^(16-r),r=0,1,2,....,16`
`rArr P(X=6)=.^16C_(6)((1)/(4))^6((3)//(4))^10`