To add to professor's explanation, another way to put it is that the Hoeffding inequality as presented in the book applies to sequence of N i.i.d. Bernoullli random variables with parameter

.

This condition can actually be relaxed to any N non-identical but independent r.v.'s that almost surely take values on compact intervals. There's even a further generalization that does not even require independence, so long as the sequence is a Martingale with (a.s.) bounded increments (see Azuma-Hoeffding inequality).