Answer :
Answer: Therefore, the total expected value of the student's score on the test is the sum of the expected values for the multiple-choice and true/false sections: 2.4 (from multiple-choice) + 1 (from true/false) = 3.4 points. Therefore, the expected value of the student's score on the test, if they randomly guess on each question, is 3.4 points.
Step-by-step explanation: To calculate the expected value of the student's score on the test, we need to determine the expected value for each type of question. For the multiple-choice questions: - Each question has 5 possible choices, so the probability of guessing the correct answer is 1/5 = 0.2. - Each question is worth 3 points, so the expected value for each multiple-choice question is 3 * 0.2 = 0.6 points. Since there are 4 multiple-choice questions, the total expected value for the multiple-choice section is 4 * 0.6 = 2.4 points. For the true/false questions: - Each question has 2 possible choices (true or false), so the probability of guessing the correct answer is 1/2 = 0.5. - Each question is worth 1 point, so the expected value for each true/false question is 1 * 0.5 = 0.5 points. Since there are 2 true/false questions, the total expected value for the true/false section is 2 * 0.5 = 1 point.
