Let X be a distance random variable whose probability distribution is defined as : $P(X=x)= \left\{\begin{matrix}0.5 & ,if & x=0\\k(x+1) & ,if & x=1\, or \, 2\\k(6-x) & ,if & x=3\, or\, 4\\0 & , & otherwise\end{matrix}\right.$ The, value of k is :

$\frac{1}{10}$ $\frac{1}{20}$ $\frac{1}{2}$ $\frac{1}{4}$

$\frac{1}{20}$