Richard has just been given a 8-question multiple-choice quiz in his history cla

Question

Richard has just been given a 8-question multiple-choice quiz in his history class. Each question hasfive 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 eight questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? 0.000 (b) What is the probability that he will answer all questions incorrectly? 0.168 (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 th binomial probability distribution table 0.832 Then use the fact that P(r 2 1)-1-D(r = 0) 0.832 Compare the two results. Should they be equa? Are they equal? If not, how do you account for the difference? They should be equal, but may not be due to table error. They should be equal, but differ substantially. They should not be equal, but are equal. They should be equal, but may differ signtly due to rounding error. (d) What is the probability that Richard will answer at least half the questions correctly? 0.046

Explanation / Answer

c) They should be equal, but may differ due to rounding error.

d) We have to find P(x 4)

P = 8C4 * 0.2^4 * 0.8^4 + ...........8C8 * 0.2^8 + 0.8^0

P = 0.056

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