Answer
$X$ has not a discrete uniform distribution because different values in its range, $\mathrm{x} 1, \mathrm{x} 2, \ldots, \mathrm{xn},$ have different probability
Work Step by Step
Random variable $X=$ hospital's number $\rightarrow x=\{1,2,3,4\}$
$$\left[\begin{array}{ccccc}{x} & {1} & {2} & {3} & {4} \\ {P(x)} & {0.238} & {0.314} & {0.254} & {0.194}\end{array}\right]$$
