A student randomly guesses at 20 multiple choice questions. Each question has four possible answers with only one being correct, and each is independent of every other question.
(a) Find the probability that the student guesses EXACTLY 4 correct.
(b) Find the probability of guessing less than 3 correctly.
(c) Find the probability of guessing more than 8 correctly.
(d) Find the probability of guessing between 4 and 6 inclusively.
(e) Would any of these be likely to occur?