Some standardized tests such as the SAT test incorporate a penalty for wrong ans

Question

Some standardized tests such as the SAT test incorporate a penalty for wrong answers. For example, a multiple choice question with 5 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 5 possible answers when a student just guesses. (That means they they answered all questions by guessing, they did not leave any blank.) Show how you got your answer. Explain what it means.

     b. Explain why there is a deduction for wrong answers. Statistics, 4th edition, Michael Sullivan, Pearson, p333  

I know that P(correct answer) 1/5 because tghere is only 1 point for correct answer

                   p(incorrect answer)= 4/5 because there are 4 possible incorrect answer

i have no clue on how p(left the blank) = 1/2 please explain

Can you also explanin what it means

Explanation / Answer

P(correct answer) = 1/5

P(incorrect answer) = 1 - 1/5 = 4/5

a) Expected number = 1 * 1/5 - 1/4 * 4/5

= 0

b) there is a deduction for wrong answers because it's a negative marking. If you guess the anser wrongly, you will get -1/4 number where as if you guess it correctly , you will get 1 number.

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