"Random" simply means unaided by any intelligent bias. Are you certain that you want to claim that the first DNA wasn't randomly formed?
No, that is NOT what random means. Sure, the word is often used by creationists as if it meant that, but they are wrong.
This is very simple. DNA formation, and evolution, are not random processes. Calculations of any odds based on randomness have no bearing on evolution or DNA.
more accurately, it means incompressible.
This means that naturally occurring bias doesn't rule out "random", of course. (Is this your definition of "random"?)