Question: In a nightmare come true, you walk in to class one day to see there is a midterm you entirely forgot about. (I actually did this in my undergrad, I don't recommend it.) The exam contains exactly one multiple-choice question with five alternatives. Only one response is claimed to be correct. If you select the correct answer you will receive an A+ in the course, but if you select one of the wrong alternatives, you will fail the course and your academic career will be over. The question and alternatives are as follows:
Who is Maximus Decimus Meridius?
a. Commander of the Armies of the North.
b. General of the Felix Legions.
c. Loyal servant to the true emperor, Marcus Aurelius.
d. Father to a murdered son, husband to a murdered wife.
e. He will have his vengeance, in this life or the next.
Because all of the alternatives seem equally correct (or incorrect), you employ the wellworn strategy of "when in doubt, choose (c)", and hope for the best. After you hand in the exam, the instructor informs you that alternatives (a), (b), and (d), were incorrect (and he would only report on incorrect alternatives). In light of that information, he offers you the possibility to change your answer of (c) to the remaining answer of (e). Aside from waking up from the nightmare, what should you do in terms of the offer, and why? (i.e., explain your reasoning probabilistically.)