Your first example is not non-deterministic, it's probabilistic. Drawing a sample from a truly random distribution doesn't make the program non-deterministic.
Non-determinism comes from transitions which have no known distribution and might cause your program to take alternate execution paths without any predefined rule. That's clearly not true in your example.
Non-determinism comes from transitions which have no known distribution and might cause your program to take alternate execution paths without any predefined rule. That's clearly not true in your example.