You are correct!
From our dictionary:
1. dependent on circumstances beyond one's control; uncertain; unstable; insecure: a precarious livelihood.
2. dependent on the will or pleasure of another; liable to be withdrawn or lost at the will of another: He held a precarious tenure under an arbitrary administration.
3. exposed to or involving danger; dangerous; perilous; risky: the precarious life of an underseas diver.
4. having insufficient, little, or no foundation: a precarious assumption.