What does it mean to "satisfy" Hoeffding's Inequality?

[gordonbr]

I'm confused about the process of determining whether a particular random sample "satisfies" Hoeffding's inequality.

In particular, when we run some experiments and determine the average proportion of green marbles, we generate some averages for several values. Can't we say that all of these values satisfy Hoeffding's Inequality, since Hoeffding's Inequality only says that the probability of something bad happening (i.e., not tracking ) for a random sample is small? I would think that any satisfies this condition, regardless of how we determined the sample.

I suppose my question is: how does a particular value fail to satisfy an inequality that seems to be a blanket statement for all possible values?