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A teacher administers a multiple choice quiz. Each question has N answers. If a student chooses the (only) correct answer, they will receive 1 point. The teacher adds that if the student circles multiple answers, they will receive partial credit based on how many they circled (only if the correct answer is circled).
If a student were to circle N (all of the answers), he would receive 0 points.
What relationship exists between the number of answers circled, and the fraction of points the professor should fairly give?