Question

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? A) 69.2 B) 90.8 C) 97.2

Answer 1

For 12 of the questions the probability of answering correctly is 1 for each of the 12. Therefore the expected score for 12 of the 25 questions is:
\[\large 12\times1\times6=72\]
For 4 of the other questions, Joe was sure that 2 of the 5 choices were not correct. He then guessed on the remaining 3 choices on each of these 4 questions. The probability of getting each of these 4 questions correct is 1/3. Therefore the expected score for these 4 questions is:
\[\large 4\times\cfrac{1}{3}\times6=8\]
For the remaining 9 questions the probability of guessing correctly for each of the 9 questions is 1/5. therefore the expected score for these 9 questions is:
\[\large 9\times\frac{1}{5}\times6=10.8\]
The expected score for the whole test is therefore given by:
72 + 8 + 10.8 = 90.8