Yesterday, Arjun also took the 2012 AMC, with similar rules to the old one (see problem #325), except “no answer” is worth $1.5$ points. This time, he answered $12$ questions with $95\%$ certainty for each problem. What is the optimal number of (whole) guesses Arjun should have made?
It turns out, Arjun did make guesses on that AMC – $3$ guesses with $40\%$ certainty of correctness. What is the probability he got over $100$?