If $X$ follows a binomial distribution with parameters $n$ and $p$. $p \lt 0 \lt 1$ If $ P(X=r)/P(X=n-r)$ is independent of $ n \:$ and$\: r$ , then value of p is :

Question

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