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Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has...

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Basic Math

Richard has just been given a 4-question multiple-choice quiz inhis history class. Each question has five answers, of which onlyone is correct. Since Richard has not attended class recently, hedoesn't know any of the answers. Assuming that Richard guesses onall four questions, find the indicated probabilities. (Round youranswers to three decimal places.)

(a) What is the probability that he will answer all questionscorrectly?


(b) What is the probability that he will answer all questionsincorrectly?


(c) What is the probability that he will answer at least one of thequestions correctly? Compute this probability two ways. First, usethe rule for mutually exclusive events and the probabilities shownin the binomial probability distribution table.


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


Compare the two results. Should they be equal? Are they equal? Ifnot, how do you account for the difference?


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

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