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# If X is a binomial variate with the range { 0,1,2,3,4,5,6 } and P(X = 2)=4P (x=4) then the parameter P of X is

$\begin {array} {1 1} (A)\;\large\frac{1}{3} & \quad (B)\;\large\frac{1}{2} \\ (C)\;\large\frac{2}{3} & \quad (D)\;\large\frac{3}{4} \end {array}$

Here $n=6$
According to the question
$6C_2P^2Q^4=4.6C_4P^4Q^2$
$Q^2=4P^2$
$(1-P)^2=4P^2$
$3P^2+2P-1=0$
$(P+1)(3P-1)=0$
$P=\large\frac{1}{3}\: \: \: P=-1$ [ P can not be negative ]
Ans : (A)