In a multiple-choice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value.

Question

In a multiple-choice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value.

Answer 1

If it is a sheer guess, the students have 4/5 chance of losing 2 points and 1/5 chance of gaining 5. Not answering is certain to get 0 points.

Does that help?

Answer 2

yes thank you.

Answer 3

To determine whether it is advantageous or disadvantageous for the student to guess an answer, we need to compare the expected values of guessing and not guessing.

Let's calculate the expected value for guessing an answer:
Since there are five options, the probability of guessing the correct answer is 1/5. Therefore, the student has a 1/5 chance of gaining 5 points and a 4/5 chance of losing 2 points.

Expected value = (Probability of gaining points * Points for gaining) + (Probability of losing points * Points for losing)
Expected value = (1/5 * 5) + (4/5 * -2)
Expected value = 1 - 1.6
Expected value = -0.6

The expected value for guessing an answer is -0.6.

Now, let's calculate the expected value for not guessing:
If the student chooses not to answer the question, they will receive no points.

Expected value = 0

Comparing the expected values, we find that the expected value for guessing (-0.6) is less than the expected value for not guessing (0). This suggests that it is disadvantageous for the student to guess an answer.