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Richard has just been given an 8 question multiple choice quiz in his history class...

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Richard has just been given an 8 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 eight questions find the indicated probabilities Round your answers to three decimal places USE SALT a What is the probability that he will answer all questions correctly 0 0000001 b What is the probability that he will answer all questions incorrectly 0 1677721 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 0 8322278 Then use the fact that P r 2 1 1 P r 0 0 8322278 Compare the two results Should they be equal Are they equal If not how do you account for the difference They should be equal but differ substantially They should be equal but may differ slightly due to rounding error They should not be equal but are equal They should be equal but may not be due to table error d What is the probability that Richard will answer at least half the questions correctly

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