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. `(9)/(16)`
B. `(3)/(4)`
C. `(1)/(16)`
D. `(15)/(16)`

Answer

D

Explanation

(d) Mean, `" "np=2 " "`…(i)
Variance, `" " npq=1 " "`……(ii)
`rArr " "q=(1)/(2)" "` [from Eqs.(i) and (ii)]
`:' " "p=1-q`
`:. " " p=(1)/(2)`
Also,`" " np=2`
`:. " " n=4`
Probability that X takes a value greater than or equal to 1
`=P(X=0)`
`=1-""^(4)C_(0)(p)^(0)q^(4)`
`=1-1.((1)/(2))^(4)=(15)/(16)`