If X is binomial variate with parameters $n$ and $p$ where $0 < P < 1$ such that $\large\frac{P(x=r)}{P(x=n-r)}$ is independent of n and r then p equals.

Question

$\begin {array} {1 1} (A)\;\large\frac{1}{2} & \quad (B)\;\large\frac{1}{3} \\ (C)\;\large\frac{1}{4} & \quad (D)\;None\: of \: these \end {array}$