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?
in general \[Expected~Value = \sum_{} x*P(x)\] so you'd need to find the probability of getting a question right * the point value for that question, repeat for all 15 questions, then sum the results he already knows he got 12 questions right, and at 6 points a piece that's 12*6 for the next 4 questions he only has a (3/5) chance of getting each one right since he eliminated 2 choices from each that gives us 4(3/5)(6) for the last remaining 9 problems, he is guessing randomly, so he only has a 1/5 chance of getting each individual question right try to compute the expected value for those 9 questions. after that, sum the products and the result should be the expected value.
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