Question

In a multiple-choice test, each question has four options. Students will get 5 points for each correct answer; lose 1 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

probability of getting the right answer is 1/4. now 1/5 of the total marks allotted to a question gets deducted. so on a large scale ( even though you asked for one problem, just for explaining) lets say he guessed 20 questions with pure guessing. so he gets 5 correct and scores 25 for them, but gets 15 wrong and so he lands up at 10 points plus. so basically he is at a advantage. (though we all know that doesnt actually happen in an actual test by guessing!! :p)