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?

Answer 1

In general, expected value = (probability of a value)(the value)

In the context of this problem, expected score = (probability of getting the question right)*(the point value of a correct answer) summed for all the questions

He says he’s sure about 12 problems, so let’s assume (100%) probability for 12 questions worth 6 points each. That’s 1 * 6 * 12 = 72 points

On 4 questions he eliminated 2 choices each, and guessed. Since each question has 5 choices, he’s guessing between 5 - 2 = 3 choices

So on those 4 questions, he had a 3/5 chance of getting each eight. So his expected score for those 4 problems is 4 * (3/5) * 6

Repeat this logic for the last 9 problems

Then add up all the expected scores