Richard has just been given a4-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 allfourquestions, find the indicated probabilities. (Round your answers to three decimal places.)

(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 thebinomial probability distribution table.

Then use the fact thatP(r1) = 1P(r= 0).

(d)What is the probability that Richard will answer at least half the questions correctly?