Create a transition system with edges $a$ and $b$ and an initial state, such that for all possible sequences, you have that: The amount of $a$'s in the sequence is at least twice as much as the amount of $b$'s in the sequence.
I'm really not sure if I did it correctly because I just had DFA and NFA and other kind of automata last semester and they still confuse me for this. My problem is, do I have to make sure that in this task that my transition system needs to create every possible sequence where we have at least twice as many $a$'s than $b$'s? Or as the task says, all I need to make sure is that for every sequence, we have that there are twice as many $a$'s than $b$'s? I think this is it and that's why I created this transition system:
Did I understand it correctly and is my transition system correct? Or do I really need to create a transition system which generates every possible combination of $a$'s and $b$'s satisfying the condition mentioned in the task? :S