Ellen is a risk-neutral test taker who has been studying for her Decision Analysis midterm. The midterm has fifteen questions, and each question has four possible answers. The midterm is different...

Ellen is a risk-neutral test taker who has been studying for her Decision Analysis midterm. The midterm has fifteen questions, and each question has four possible answers. The midterm is different from any she has taken before. Instead of just marking the answer she thinks is correct—a, b, c, or d—she assigns a probability to the chance that each answer is correct. The sum of the probabilities she assigns for each question must equal one. The following formula is used to score each question (normalized for a possible 100 points on the exam):

where p is the probability she assigns to the correct answer.