This is a good question. The correct answer is:
"Are you one of those people who think that accidents never happen?"
What we have here is a relative clause and you are asked to give the proper form of the relative pronoun. The way to go about doing this is the locate the relative clause and examine its grammar. The relative pronoun, which starts off the relative clause, will take its grammatical function from its relation within the relative clause and not the sentence.
Since the relative clause needs a subject, the correct relative pronoun must be in the subject case. This is why the answer is "who." Finally, do not let the interrogative throw you off. Interrogative sentences work the same way in terms of grammar - there are subjects, verbs, and objects.