This question, in my opinion, is a bit misleading. From what I understand it is just asking if the outcome of the XOR 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.
