On a quiz there are four multiple-choice questions, worth three points each and two true false questions worth 1.8 each multiple-choice question has five possible choices. If a student randomly guesses on each question, what is the expected value of the student score on the test?

Answer 1

To find the expected value of the student's score on the test, we need to calculate the expected score for each type of question separately and then add them all together.

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 correct answer is worth 3 points, so the expected score for each multiple-choice question is 3 * 0.2 = 0.6 points
- Since there are 4 multiple-choice questions, the total expected score for these questions is 4 * 0.6 = 2.4 points

For the true/false questions:
- There are 2 true/false questions, so the probability of guessing the correct answer is 0.5
- Each correct answer is worth 1.8 points, so the expected score for each true/false question is 1.8 * 0.5 = 0.9 points
- Since there are 2 true/false questions, the total expected score for these questions is 2 * 0.9 = 1.8 points

Therefore, the total expected value of the student's score on the test is 2.4 (from the multiple-choice questions) + 1.8 (from the true/false questions) = 4.2 points.