In a multiple-choice test, each question has four options. Students will get 2 p

Question

In a multiple-choice test, each question has four options. Students will get 2 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.

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Explanation / Answer

This is known as an "Expected Value" problem. Assuming he/she guesses at a question: Correct answer >>> 1/5 * 2 points = 2/5 Incorrect answer >> 4/5 * -1 point = -4/5 Unanswered question = 0 points = 0 Expected Value = 2/5 + (-4/5) + 0 Expected Value = -2/5 Therefore the student can expect to LOSE on average 2/5th of a point each time he/she guesses at a problem.

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