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
I would say that it is to her disadvantage because if you guess an answer and get it wrong then you lose 2 points but if you don't put anything then you don't gain any points or lose any points. There is a chance she would most likely get it wrong if she guessed, So i would have to say not guessing is the better way to go if you arent going to lose any points for putting no answer.
This was a really confusing question so im not sure that my answer is correct but i tried answering it as best as i could... sorry :(
But actually now that i think of it, i think im right because she has a 75% chance its wrong. And she would lose 2 points.
To determine whether it is advantageous for the student to guess an answer or not, we can calculate the expected value for both scenarios: guessing an answer and leaving it unanswered.
Let's start by calculating the expected value if the student guesses an answer:
Probability of guessing the correct answer: 1/5
Points for a correct answer: 5
Expected value for a correct guess: (1/5) * 5 = 1
Probability of guessing an incorrect answer: 4/5
Points deducted for an incorrect answer: -2
Expected value for an incorrect guess: (4/5) * (-2) = -8/5
Therefore, the expected value for guessing an answer can be calculated as follows:
Expected value for guessing = (Probability of guessing a correct answer * Points for a correct answer) + (Probability of guessing an incorrect answer * Points deducted for an incorrect answer)
Expected value for guessing = (1/5 * 5) + (4/5 * -2)
Expected value for guessing = 1 + (-8/5)
Expected value for guessing = -3/5
Since the expected value for guessing an answer is negative (-3/5), it means that on average, the student will lose 3/5 (or 0.6) points per question if they choose to guess.
Now let's calculate the expected value if the student leaves the question unanswered:
Probability of leaving the question unanswered: 1
Points for leaving the question unanswered: 0
Expected value for leaving the question unanswered: (1 * 0) = 0
The expected value for leaving the question unanswered is 0, meaning the student neither gains nor loses points on average.
Comparing the two expected values, we see that the expected value for guessing is negative (-3/5 or -0.6), indicating that the student will lose points on average if they guess. On the other hand, leaving the question unanswered has an expected value of 0, meaning the student neither gains nor loses points. Therefore, it would be in the student's advantage to leave the question unanswered.