Some standardized tests, such as the SAT test, incorporate a penalty for wrong answers. For example, a multiple-choice question with ﬁve possible answers will have 1 point awarded for a correct answer and 1 4 point deducted for an
incorrect answer. Questions left blank are worth 0 points.
(a) Find the expected number of points received for a multiple-choice question with ﬁve possible answers when a student just guesses.
(b) Explain why there is a deduction for wrong answers.