A 50-question true-false examination is given. Each correct answer is worth 10 points. Consider an unprepared student who randomly guesses on each question.
a. If no points are deducted for incorrect answers, what is the probability that the student will score at least 350 points?
b. If 5 points are deducted for each incorrect answer, what is the probability that the student will score at least 200 points?
c. If 10 points are deducted for each incorrect answer, what is the probability that the student will receive a negative score?