DFA and equivalence classes: counting odd numbers of b's
Your first and third equivalence classes are equivalent to one another. They both contain strings in which there are an even number of $b$s: in the first class, that number is zero; in the third class, it's at least two.  For any string in either of those classes, adding a string with an odd number of $b$s gives a string in the language, and adding a string with an even number gives a string not in it.