Assume you are taking a multiple-choice exam that contains 10 questions. Each qu

Question

Assume you are taking a multiple-choice exam that contains 10 questions. Each question has 5 possible answers. You are a good student, and are confident about your answers to 7 of the 10 questions. You have a 0 .96probability that you answered correctly on each of these 7 questions. You are clueless about the remaining 3 questions, and randomly chose answers for these 3 questions.

• Assume each correct question is worth 1 point, and each incorrect question is worth 0 points. What is the expected value of your score on the exam?

• Assume each correct question is worth 1 point, and each incorrect question is worth 0 .25 points. What is the expected value of your score on the exam?

Explanation / Answer

7 qns right and 3 wrong

Prob for a guess to be right = 1/5

wrong = 4/5

R,W = (7,3) (8,2) (9,1) (10,0)

Prob 0.512 0.384 0.096 0.008

Marks 7 8 9 10

Marks*p 3.584 3.072 0.864 0.08 Total 7.6

Expected score =7.60

-----------------------------------

If negative mark is there 3 questions unknown may be right or wrong.

R,W = (7,3) (8,2) (9,1) (10,0)

Prob 0.512 0.384 0.096 0.008

Marks 6.25 7.50 8.75 10

Marks*p 3.2 2.88 0.756 0.08 Total 6.916

Expected score =6.916

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.