PAC learning axis parallel rectangles
The question is a little vague, but it seems like what you want to argue is along the line of this: Let $R$ be the concept to learn, and take any $R^*\subset R$ be any rectangle covering a $(1-\epsilon)$-fraction of $R$.  Then with some probability $R'$ will contain $R^*$.

The problem with this is that the particular probability depends on the specific choice of $R^*$.  I think what you're confused about is that want $R'$ to perform well on unseen examples.  By construction $R'$ will correctly classify all the training data.  The bad event is actually that all of the training data is concentrated in too small a rectangle; this happens with probability at most that of the event that one of the strips is missed by all the training examples.