Richard has just been given a 8 -question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct.

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(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 the binomial probability distribution table.

Then use the fact that P(r ≥ 1) = 1 − P(r = 0).