Question 8.94

image 63. On five-choice questions on the SAT, you get 1 point for a correct answer and lose point for a wrong answer.

  1. Find the expected value of a completely random guess on such a question. Does guessing in this situation help you, hurt you, or make no difference?
  2. Suppose you eliminate one of the five choices as definitely not being the correct answer and then randomly guess among the remaining four choices. Does guessing in this situation help you, hurt you, or make no difference?

63.

(a) The expected value on a single question is . Thus, random guessing makes no difference.

(b) The expected value on a single question is now .

Thus, guessing will increase your score on average.