Answer
$0.55$
Work Step by Step
$x^2-6x+c=(x-3)^2-9+c$
As we can see, the vertex will be at $x=3$ where $(x-3)^2$ has its minimum value ($0$), and the vertex will have a $y$ value of $y=-9+c.$
This will be positive for $10\leq c\leq20$, thus for $11$ values of $c$ (because $c$ is an integer).
Thus the probability is: $\frac{11}{20}=0.55$
