Assume that the test has 5 true/false questions, and 10 multiple choice questions (4 options per questions), each with exactly one correct answer.

If a student guesses randomly on each question, what is his expected score?

.5*5+10*.25

5/15?

To calculate the student's expected score, you need to determine the probability of getting each question correct and then multiply it by the corresponding point value.

For the true/false questions, there are only two possible outcomes: correct or incorrect. Since the student is guessing randomly, the probability of getting a true/false question correct is 1/2 or 0.5. Therefore, the student's score for the true/false section would be 0.5 multiplied by the number of questions, which is 5. This gives us a score of 2.5 for the true/false section.

For the multiple-choice questions, there are 4 possible options, but only 1 correct answer. Since the student is guessing randomly, the probability of getting a multiple-choice question correct is 1/4 or 0.25. Therefore, the student's score for the multiple-choice section would be 0.25 multiplied by the number of questions, which is 10. This gives us a score of 2.5 for the multiple-choice section.

To calculate the expected score, you add the scores for each section together:

Expected score = Score for true/false section + Score for multiple-choice section
Expected score = 2.5 + 2.5
Expected score = 5

Therefore, the student's expected score, if guessing randomly on each question, is 5.