Ellen is a risk-neutral test taker who has been studying for her Decision Analysis midterm. The…

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):

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