I thought this was a trick question since skin cancers are the most common type of cancers overall. But actually among HIV patients, HIV-related cancers are much more common than non-HIV-related cancers (even skin cancers). EBV-induced primary CNS lymphoma is the only option that is AIDs-defining illness/cancer.

EBV virus infections B cells. As a response there is reactive lymphocytosis (proliferation of CD8+ cytotoxic T Lymphocytes). In HIV, you will have a decrease in TH cells leading to decrease in CD8 T cells. Thus EBV will proliferate more freely as the immune response towards it (CD8 cells) are blunted. This is how i got to the answer.