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The correct answer is option 3, Herta Mueller. In the paragraph, it is mentioned that the person being referred to is a member of Romania`s ethnic German minority who was prosecuted for her critical depictions of life `Behind the Iron Curtain`. Herta Mueller is a Romanian-born German novelist and poet of German descent. She is widely known for her critical depictions of life under the communist regime in Romania. She was awarded the Nobel Prize in Literature in 2009 for her work.
Option 1, Doris Lessing, is incorrect because she was a British novelist who won the Nobel Prize in Literature in 2007, but she is not associated with Romania or the German minority there.
Option 2, Gunter Grass, is incorrect because he was a German novelist and playwright associated with Germany, not Romania.
Option 4, Imre Kertesz, is incorrect because he was a Hungarian writer and Holocaust survivor who won the Nobel Prize in Literature in 2002, but he is not associated with Romania or the German minority there.
Therefore, the correct answer is option 3, Herta Mueller.