10
lesson pretestMultiple Choice

Pretest

Question 10 • Mathematics III

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 point 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?

Answer
A
75 point 6
B
69 point 2
C
97 point 2
D
90 point 8

Explanation

Joe earns 12 × 6 = 72 points for the answers he knows. On each of the 4 questions where he eliminates 2 choices, his chance of being correct is 1/3, so those questions contribute 4 × (1/3 × 6) = 8 expected points. On each of the other 9 questions, his chance is 1/5, contributing 9 × (1/5 × 6) = 10.8 expected points. His expected total is 72 + 8 + 10.8 = 90.8 points, choice D.

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