This question, in my opinion, is a bit misleading. From what I understand it is just asking if the outcome is independent of the bits if they are biased. If both bits are biased, then they both have the same chance, $ '''p''' $, of being 1 and the same chance, $ '''1-p''' $, of being 0.
So, since A and B have the same chances then, by definition, they are independent, and A XOR B is also independent of each individual bit.
