Question

Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has four 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?

(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). _____________

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

(please explain the steps used to solve these)

Answer #1

Richard has just been given a 4-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 four questions, 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...

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

Richard has just been given a 10-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 ten questions, find the indicated probabilities. (Round your
answers to three decimal places.)
What is the probability that Richard will answer at least half
the questions correctly?

A student has just been given a 10-question multiple-choice
quiz. Each question has five answers, of which only one is correct.
The student has not attended class recently, and doesn't know any
of the answers. Assume that guesses are made on all ten questions,
find the indicated probability. (Round your answer to three decimal
places.) What is the probability that the student will answer all
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b. 0.8154
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