## Problem of the Day #326: Post-AMC Woes
*February 8, 2012*

*Posted by Albert in : potd , trackback*

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 $100$?

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