Arjun is taking an old AMC, a 25-question contest where a correct answer earns $6$ points, no answer earns $2.5$ points, and an incorrect answer earns $0$ points. Given that Arjun is $90\%$ sure of his $10$ answered questions and that there is $1$ minute left, on how many questions should Arjun guess (chance correct per question = $20\%$) to maximize his probability of getting a score of over $100$? What is this probability?