When answering a question on a multiple choice exam, Jon eitherthinks he knows the answer or just guesses.
Suppose the probability that Jon thinks he knows the answer is0.75 and there’s a 90% chance that he’ll get the question correctif he thinks he knows the answer. There are 5 choices for eachmultiple-choice exam question.
Each question is worth 2 marks (no part marks), but blankanswers earn 0.4 marks. Suppose Jon always answers the question ifhe thinks he knows the answer, but if he does not, he guesses theanswer (at random) half the time and the other half of the time, heleaves the answer blank.
What is the expected value of Jon’s score on a randomly selectedquestion?
