Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 10 questions, find the indicated probabilities.
(a) What is the probability that he will answer all questions correctly?
(b) What is the probability that he will answer all questions incorrectly?
(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in Table 2 of the Appendix. Then use the fact that P(r ≥ 1) = 1 – P(r = 0). Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?
(d) What is the probability that Richard will answer at least half the questions correctly?