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When a question like this is asked in a headline, you know the answer is, "No, my Facebook profile is not as private as I think."
On whether or not third parties can gather data from quiz answers, Tim Sparapani, director of public policy at Facebook, said Facebook would never let that happen. Such conduct is shut down and strictly enforced. However... "He won't cite a specific case of such enforcement, but he says it has happened."
Okay, we can all rest assured.
Me: Say, police officer, have you ever stopped a murder from happening?
Cop: Oh, of course, it's my job.
Me: Cool! Please, tell me a story.
Cop: Er, um, well, I don't have a story, but I have done it.
Me: Gee, seems like it would be a memorable experience, but I'll take your word for it!