Question: In Problem, keep the number of choices given with each question at four, but suppose now there are ten questions. Answer the questions posed in Problem, and also determine the probability of getting five, six, or seven questions correct.
Problem: A professor gives a test consisting of six multiple choice questions, each offering four answers from which to choose. A student who knows less than nothing takes the test by the method of random choice, simply guessing on each question.
(a) What is the probability that the student gets exactly one question right?
(b) What is the probability of getting exactly two right?
(c) What is the probability of getting four or five right?
(d) What is the probability of getting all six questions right?