I had unprotected sex with a person that had an std. Is there any chance I did not get a std?

STD. There is a chance you did contract the illness and a chance you did not, consult with your doctor to determine the result. Best.
Sure. Yes, not all people will get the std that their partner had, but very risky and not to be counted upon. Protect yourself always and if concerned about exposure - get tested asap!