What Are The Chances Of THC Being Found In Blood On Miniscule Intake?

Hello, I smoked marijuana 6 days ago. It was a very very small amount. It was my first time trying it and needless to say I didn t like it at all, so that is why I only had a miniscule intake. Anyways, I am going to get a blood titer tomorrow and I was wondering if there would be a chance of THC being found in my blood work. Or does the doctor have to separately test for that?