Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score?

Joe earns 12 × 6 = 72 points from the answers he is sure of. On each of the 4 questions where he eliminated 2 choices, his chance of being correct is 1/3, so the expected points per question are (1/3) × 6 = 2, for 8 points total. On each of the remaining 9 questions, his chance is 1/5, giving (1/5) × 6 = 1.2 expected points each, or 10.8 points total. His expected score is 72 + 8 + 10.8 = 90.8, choice C.

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