。
Is she so foolish as to believe such a thing?
Literal
She [topic-は] that-kind-of thing [object-を] believe [to-the-extent-of-ほど] foolish-is [explanatory question-のですか]?
[verb-clause]+ほど+[adjective] gives 'X enough to do Y,' setting a threshold of degree — here そんなことを信じるほどばか ('foolish enough to believe such a thing') uses the embedded clause as the bar to be measured against. The ending のですか combines explanatory のだ with the question particle か, making it a polite probing question rather than a flat one — 'is it really the case that...?' The whole sentence is a rhetorical-leaning question, more often asked to express disbelief than to gather information.